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Publikationen 2013

W. Alt, R. Baier, M. Gerdts, F. Lempio: Approximation of Linear Control Problems with Bang-Bang Solutions
Optimization 62 (1), 9 - 32, 2013, online available in iFirst since May 2011

DOI: 10.1080/02331934.2011.568619

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N. Altmüller, L. Grüne: A comparative stability analysis of Neumann and Dirichlet boundary MPC for the heat equation
in: Proceedings of the 1st IFAC Workshop on Control of Systems Modeled by Partial Differential Equations - CPDE 2013, 2013, 161 - 166, Paper #48

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R. Baier, E. Farkhi: Regularity of set-valued maps and their selections through set differences. Part 1: Lipschitz continuity
Serdica Mathematical Journal 39 (3-4), 365 - 390, 2013, Special issue dedicated to the 65th anniversary of Professor Asen L. Dontchev and to the 60th anniversary of Professor Vladimir M. Veliov.

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R. Baier, E. Farkhi: Regularity of set-valued maps and their selections through set differences. Part 2: One-sided Lipschitz properties
Serdica Mathematical Journal 39 (3-4), 391 - 422, 2013, Special issue dedicated to the 65th anniversary of Professor Asen L. Dontchev and to the 60th anniversary of Professor Vladimir M. Veliov. 

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R. Baier, M. Gerdts, I. Xausa: Approximation of Reachable Sets using Optimal Control Algorithms
Numerical Algebra, Control and Optimization 3 (3), 519 - 548, 2013,  

DOI: 10.3934/naco.2013.3.519

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M. Gerdts,I. Xausa: Avoidance trajectories using reachable sets and parametric sensitivity analysis
in: System modeling and optimization. 25th IFIP TC 7 conference on system modeling and optimization, CSMO 2011, Berlin, Germany, September 12–16, 2011. Revised Selected Papers, D. Hömberg, F. Tröltzsch (eds.)
IFIP Advances in Information and Communication Technology 391, 2013, 491 - 500

DOI: 10.1007/978-3-642-36062-6_49

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L. Grüne: Economic receding horizon control without terminal constraints
Automatica, 49, 725 - 734, 2013

DOI: 10.1016/j.automatica.2012.12.003
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L. Grüne, I. Karafyllis: Lyapunov function based step size control for numerical ODE solvers with application to optimization algorithms
in: Mathematical System Theory - Festschrift in Honor of Uwe Helmke on the Occasion of his 60th Birthday, K. Hüper and J. Trumpf (ed.)
CreateSpace, 2013, 183 - 210

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L. Grüne, M. Sigurani: Numerical ISS controller design via a dynamic game approach
in: Proceedings of the 52nd IEEE Conference on Decision and Control - CDC 2013, 2013, 1732 - 1737

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Publikationen 2012

W. Alt, R. Baier, M. Gerdts, F. Lempio: Error bounds for Euler approximation of linear-quadratic control problems with bang-bang solutions
Numerical Algebra, Control and Optimization 2 (3), 547 - 570, 2012,

A special issue Dedicated to Professor Helmut Maurer on the occasion of his 65th birthday. Submitted in July 2011.

DOI: 10.3934/naco.2012.2.547
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N. Altmüller, L. Grüne: Distributed and boundary model predictive control for the heat equation
GAMM Mitteilungen 35 (2), 131 - 145, 2012

DOI: 10.1002/gamm.201210010
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R. Baier: Set-valued Euler's method with interpolated distance functions and optimal control solvers
in: Proceedings on the 20th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2012), July 9-13, 2012, Melbourne, Australia, Melbourne, Australia, 2012, 4 pages, CD-ROM, Paper No. 85, extended abstract

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R. Baier, Q. Din, T. D. Donchev: Higher Order Runge-Kutta Methods for Impulsive Differential Systems
Applied Mathematics and Computation, 218, (24), 11790 - 11798, 2012

DOI: 10.1016/j.amc.2012.05.037

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R. Baier, E. Farkhi, V. Roshchina: The Directed and Rubinov Subdifferentials of Quasidifferentiable Functions. Part I: Definition and Examples
Nonlinear Analysis: Theory, Methods & Applications 75 (3), 1074 - 1088, 2012

DOI: 10.1016/j.na.2011.04.074
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R. Baier, E. Farkhi, V. Roshchina: The Directed and Rubinov Subdifferentials of Quasidifferentiable Functions. Part II: Calculus
Nonlinear Analysis: Theory, Methods & Applications 75 (3), 1058 - 1073, 2012

DOI: 10.1016/j.na.2011.04.073
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R. Baier, L. Grüne, S.F. Hafstein: Linear programming based Lyapunov function computation for differential inclusions
Discrete and Continuous Dynamical Systems- Series B 17 (1), 33 - 56, 2012

DOI: 10.3934/dcdsb.2012.17.33
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R. Baier, M. Hessel-von Molo: Newton's method and secant method for set-valued mappings
in: Proceedings on the 8th International Conference on "Large-Scale Scientific Computations" (LSSC 2011), Sozopol, Bulgaria, June 6-10, 2011. Revised Selected Papers, I. Lirkov, S. Margenov, J. Wanśiewski (eds.)
Lecture Notes in Computer Science 7116, Springer-Verlag, Berlin-Heidelberg, 2012, 91 - 98

DOI: 10.1007/978-3-642-29843-1_9
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P. Braun, J. Pannek, K. Worthmann: Predictive Control Algorithms: Stability despite Shortened Optimization Horizons
in: Proceedings on the 15-th IFAC Workshop on Control Applications of Optimization CAO'2012, Rimini, Italy, 2012, 284 - 289

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I. Kornienko, M. Gerdts, M. de Pinho: A new version of necessary conditions for optimal control problems with differential algebraic equations
in: Proceedings on the 20th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2012), July 9-13, 2012, Melbourne, Australia, Melbourne, Australia, 2012, 8 pages, CD-ROM, Paper No. 43, full paper

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L. Grüne: Economic MPC and the role of exponential turnpike properties
in: Oberwolfach Reports, 2012, 678-681

DOI: 10.4171/OWR/2012/12
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L. Grüne: Economic MPC without terminal constraints
Extended Abstract
in: Proceedings of the 20th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2012), 2012, CD-ROM, Paper No. 58, 4 pages

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L. Grüne: NMPC without terminal constraints
in: Proceedings of the IFAC Conference on Nonlinear Model Predictive Control 2012 (NMPC'12), 2012, 1 - 13

DOI: 10.3182/20120823-5-NL-3013.00030
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L. Grüne, T. Jahn: Computing reachable sets via barrier methods on SIMD architectures
in: Proceedings of the 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), J. Eberhardsteiner, H.J. Böhm, F.G. Rammerstorfer (eds.)
Vienna University of Technology, Vienna, Austria, 2012, CD-ROM, Paper No. 1518, 20 pages

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L. Grüne, J. Pannek, M. Seehafer, K. Worthmann: Analysis of Unconstrained Nonlinear MPC Schemes with Time Varying Control Horizon
in: Proceedings of the 51st IEEE Conference on Decision and Control, Maui, Hawaii, 2012, 2605 - 2610

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L. Grüne, J. Pannek, K. Worthmann: Ensuring Stability in Networked Systems with Nonlinear MPC for Continuous Time Systems
in: Proceedings of the 51st IEEE Conference on Decision and Control, Maui, Hawaii, 2012, 14 - 19

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L. Grüne, K. Worthmann: A distributed NMPC scheme without stabilizing terminal constraints
in: Distributed Decision Making and Control, Chapter 12, R. Johansson, A. Rantzer (eds.)
Springer Verlag, 2012, 259 - 285

DOI: 10.1007/978-1-4471-2265-4_12
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M. Hänel, S. Kuhn, D. Henrich, L. Grüne, J. Pannek: Optimal camera placement to measure distances conservatively regarding static and dynamic obstacles
Int. J. Sensor Networks 12 (1), 25 - 36, 2012

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H. Li, F. Wirth: Zubov's method for interconnected systems - a dissipative formulation
in: Proceedings on the 20th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2012), July 9-13, 2012, Melbourne, Australia, Melbourne, Australia, 2012, 8 pages, CD-ROM, Paper No. 184, full paper

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V. Palma, L. Grüne: Stability, performance and robustness of sensitivity-based multistep feedback NMPC
Extended Abstract
in: Proceedings of the 20th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2012), 2012, CD-ROM, Paper No. 68, 4 pages

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K. Worthmann: Estimates on the Prediction Horizon Length in Model Predictive Control
in: Proceedings of the 20th International Symposium on Mathematical Theory of Networks and Systems (MTNS2012), Melbourne, Australia, 2012, MTNS2012_0112_paper.pdf

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K. Worthmann: Estimates of the Prediction Horizon Length in MPC: a Numerical Case Study
in: Proceedings of the IFAC Conference on Nonlinear Model Predictive Control 2012 (NMPC'12), Noordwijkerhout, the Netherlands, 2012, 0037.pdf

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I. Xausa, R. Baier, M. Gerdts, M. Gonter, C. Wegwerth: Avoidance trajectories for driver assistance systems via solvers for optimal control problems
in: Proceedings of the 20th International Symposium on Mathematical Theory of Networks and Systems (MTNS2012), 8 pages, Melbourne, Australia, 2012, CD-ROM, Paper No. 294, full paper

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Publikationen 2011

H. Aoyama, L. Grüne, W. Semmler, Y. Fujiwara, W. Souma: Fluctuation of firm size in the long-run and bimodal distribution
Advances in Operations Research 2011, 21 pages, 2011, Article ID 269239

DOI: 10.1155/2011/269239
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R. Baier, M. Gerdts, I. Xausa: Approximation of Reachable Sets using Optimal Control Algorithms
36 pages, University of Bayreuth, Germany, 2011, technical report, October 2011, updated from version in April 26, 2010

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R. Baier, G. Perria: Set-Valued Hermite Interpolation
Journal of Approximation Theory 163 (10), 1349 - 1372, 2011

DOI: 10.1016/j.jat.2010.11.004
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P. Benner, T. Breiten, T. Damm: Generalized tangential interpolation for model reduction of discrete-time MIMO bilinear systems
Int. J. Control 84 (8), 1398 - 1407, 2011, to appear

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P. Benner, T. Damm: Lyapunov equations, energy functionals, and model order reduction of bilinear and stochastic systems
SIAM Journal on Control and Optimization 49 (2), 686 - 711, 2011

DOI: 10.1137/09075041X

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R. Findeisen, L. Grüne, J. Pannek, P. Varutti: Robustness of prediction based delay compensation for nonlinear systems
in: Proceedings of the 18th IFAC World Congress, Milano, Italy, 2011, 203 - 208

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M. Gerdts, F. Lempio: Mathematische Optimierungsverfahren des Operations Research
in: De Gruyter Studium, De Gruyter Verlag, Berlin, Germany, 2011, ix + 527 pages

DOI: 10.1515/9783110249989

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L. Grüne: Optimal invariance via receding horizon control
in: Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference, Orlando, Florida, USA, 2011, 2668 - 2673

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L. Grüne, J. Pannek: Nonlinear Model Predictive Control: Theory and Algorithms
in: xii + 370 pages, Communications and Control Engineering, Springer Verlag, 2011, xii + 370 pages

DOI: 10.1007/978-0-85729-501-9

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L. Grüne, O.S.Serea: Differential games and Zubov's method
SIAM Journal on Control and Optimization 49 (6), 2349 - 2377, 2011

DOI: 10.1137/100787829
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T. Jahn, J. Pannek: Stability of Constrained Adaptive Model Predictive Control Algorithms
in: Proceedings of the 18th IFAC World Congress, Milano, Italy, 2011, 9272 - 9277

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I. Karafyllis, L. Grüne: Feedback stabilization methods for the numerical solution of systems of ordinary differential equations
Discrete and Continuous Dynamical Systems - Series B 16 (1), 283 - 317, 2011

DOI: 10.3934/dcdsb.2011.16.283
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J. Pannek, K. Worthmann: Reducing the Prediction Horizon in NMPC: An Algorithm Based Approach
in: Proceedings of the 18th IFAC World Congress, Milano, Italy, 2011, 7969 - 7974

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K. Worthmann: Stability Analysis of Unconstrained Receding Horizon Control Schemes
Dissertation, Bayreuth, Germany, 2011

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Publikationen 2010

N. Altmüller, L. Grüne, K. Worthmann: Instantaneous control of the linear wave equation
in: Proceedings of the 18th International Symposium on Mathematical Theory of Networks and Systems (MTNS2010), Budapest, Hungary, 2010, 1895 - 1899

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N. Altmüller, L. Grüne, K. Worthmann: Performance of NMPC schemes without stabilizing terminal constraints
in: Recent Advances in Optimization and its Applications in Engineering, M. Diehl, F. Glineur, E. Jarlebring, W. Michiels (eds.)
Springer Verlag, 2010, 289 - 298

DOI: 10.1007/978-3-642-12598-0_25
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N. Altmüller, L. Grüne, K. Worthmann: Receding Horizon optimal control for the wave equation
in: Proceedings of the 49th IEEE Conference on Decision and Control, Atlanta, Georgia, 2010, 3427 - 3432

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R. Baier, T. D. Donchev: Discrete Approximation of Impulsive Differential Inclusions
Numerical Functional Analysis and Optimization 31 (6), 653 - 678, 2010

DOI: 10.1080/01630563.2010.483878
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R. Baier, E. Farkhi: The Directed Subdifferential of DC functions
in: Nonlinear Analysis and Optimization II: Optimization. A Conference in Celebration of Alex Ioffe's 70th and Simeon Reich's 60th Birthdays, June 18--24, 2008, Haifa, Israel, A. Leizarowitz, B. S. Mordukhovich, I. Shafrir, A. J. Zaslavski (eds.)
AMS Contemporary Mathematics 514, 2010, 27 - 43

DOI: 10.1090/conm/514
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R. Baier, E. Farkhi, V. Roshchina: On Computing the Mordukhovich Subdifferential Using Directed Sets in Two Dimensions
in: Special Volume "Variational Analysis and Generalized Differentiation in Optimization and Control: In Honor of Boris S. Mordukhovich". The International Symposium on "Variational Analysis and Optimization", held on November 28-30, 2008 at the Departme, Springer Optimization and Its Applications 47, New York-Dordrecht-Heidelberg-London, 2010, 59 - 93

DOI: 10.1007/978-1-4419-0437-9_3
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R. Baier, L. Grüne, S.F. Hafstein: Computing Lyapunov functions for strongly asymptotically stable differential inclusions
in: Proceedings of NOLCOS 2010, Bologna, Italy, 2010, 1098 - 1103

DOI: 10.3182/20100901-3-IT-2016.00132
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L. Grüne: Worst case vs. average performance estimates for unconstrained NMPC schemes
in: Proceedings of the GAMM Annual Meeting, Karlsruhe, Germany, 2010, 607 - 608

DOI: 10.1002/pamm.201010296
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J. Fischer: Optimal Control Problems Governed by Nonlinear Partial Differential Equations and Inclusions
Dissertation, Department of Mathematics, University of Bayreuth,
Bayreuth, Germany, 2010

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A. Greiner, L. Grüne,W. Semmler: Growth and climate change: threshold and multiple equilibria
in: Dynamic Systems, Economic Growth, and the Environment, J. Crespo Cuaresma, T. P. Palokangas, A. Tarasyev (eds.)
Springer Verlag, 2010, 63 - 79

DOI: 10.1007/978-3-642-02132-9_4
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L. Grüne, S. Jerg, O. Junge, D. Lehmann, J. Lunze, F. Müller, M. Post: Two complementary approaches to event-based control
at-Automatisierungstechnik 58 (Special Issue on Networked Control Systems), 173 - 182, 2010

DOI: 10.1524/auto.2010.0832
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L. Grüne, F. Müller: Global optimal control of quantized systems
in: Proceedings of the 18th International Symposium on Mathematical Theory of Networks and Systems (MTNS2010), Budapest, Hungary, 2010, 1231 - 1237

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L. Grüne, J. Pannek: Analysis of unconstrained NMPC schemes with incomplete optimization
in: Proceedings of NOLCOS 2010, Bologna, Italy, 2010, 238 - 243

DOI: 10.3182/20100901-3-IT-2016.00124
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L. Grüne, J. Pannek, M. Seehafer, K. Worthmann: Analysis of unconstrained nonlinear MPC schemes with varying control horizon
SIAM Journal on Control and Optimization 48 (8), 4938 - 4962, 2010

DOI: 10.1137/090758696
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L. Grüne, S. Sager, F. Allgöwer, H. G. Bock, M. Diehl: Predictive planning and systematic action - on the control of technical processes
in: Production Factor Mathematics, M.Grötschel, K. Lucas, V. Mehrmann (eds.)
Springer Verlag, 2010, 9 - 37

DOI: 10.1007/978-3-642-11248-5_2
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L. Grüne, M. von Lossow, J. Pannek, K. Worthmann: MPC: implications of a growth condition on exponentially controllable systems
in: Proceedings of NOLCOS 2010, Bologna, Italy, 2010, 385 - 390

DOI: 10.3182/20100901-3-IT-2016.00225
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L. Grüne, M. von Lossow, K. Worthmann: NMPC suboptimality estimates for sampled-data continuous systems
in: Recent Advances in Optimization and its Applications in Engineering, M. Diehl, F. Glineur, E. Jarlebring, W. Michiels (eds.)
Springer Verlag, 2010, 329 - 338

DOI: 10.1007/978-3-642-12598-0_29
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T. Jahn: Implementierung numerischer Algorithmen auf CUDA–Systemen
Diplomarbeit, Universität Bayreuth, Germany, 2010

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Publikationen 2009

R. Baier, T. D. Donchev: Discrete Approximation of Impulsive Differential Inclusions
22 pages, University of Bonn, September 2009

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R. Baier, M. Gerdts: A Computational Method for Non-Convex Reachable Sets using Optimal Control
in: Proceedings of the European Control Conference (ECC) 2009, August 23-26, session MoA2.6, EUCA, Budapest, Hungary, 2009, 97 - 102

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F. Camilli, L. Grüne, F. Wirth: Domains of attraction of interconnected systems: A Zubov method approach
in: Proceedings of the European Control Conference (ECC) 2009, Budapest, Hungary, 2009, 91 - 96

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L. Grüne: Analysis and design of unconstrained nonlinear MPC schemes for finite and infinite dimensional systems
SIAM Journal on Control and Optimization 48, 1206 - 1228, 2009

DOI: 10.1137/070707853
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L. Grüne, O. Junge: Gewöhnliche Differentialgleichungen - Eine Einführung aus der Perspektive der Dynamischen Systeme
Vieweg + Teubner Verlag, 2009,

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L. Grüne, O. Junge: Set oriented construction of globally optimal controllers
at-Automatisierungstechnik 57, 287 - 295, 2009

DOI: 10.1524/auto.2009.0777
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L. Grüne, I. Karafyllis: Feedback stabilization methods for the numerical solution of systems of ordinary differential equations
in: Proceedings of the International Conference on Numerical Analysis ans Applied Mathematics ICNAAM 2009, AIP Conference Proceedings 1168, Rethymno, Crete, Greece, 2009, 152 - 155

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L. Grüne, F. Müller: An algorithm for event-based optimal feedback control
in: Proceedings of the 48th IEEE Conference on Decision and Control, Shanghai, China, 2009, 5311 - 5316

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L. Grüne, D. Nesic, K. Worthmann: Digital redesign of nonlinear multi-input systems
in: Oberwolfach Reports 11, 2009, 619 - 622

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L. Grüne, J. Pannek: Practical NMPC suboptimality estimates along trajectories
Systems & Control Letters 58, 161 - 168, 2009

DOI: 10.1016/j.sysconle.2008.10.012
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L. Grüne, J. Pannek, K. Worthmann: A networked unconstrained nonlinear MPC scheme
in: Proceedings of the European Control Conference (ECC) 2009, Budapest, Hungary, 2009, 371 - 376

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L. Grüne, J. Pannek, K. Worthmann: A prediction based control scheme for networked systems with delays and packet dropouts
in: Proceedings of the 48th IEEE Conference on Decision and Control, Shanghai, China, 2009, 537 - 542

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L. Grüne, S. Sager, F. Allgöwer, H. G. Bock, M. Diehl: Vorausschauend planen, gezielt handeln - über die Regelung und Steuerung technischer Prozesse
in: Produktionsfaktor Mathematik, M. Grötschel, K. Lucas, V. Mehrmann (eds.)
Springer Verlag, 2009, 27 - 62

DOI: 10.1007/978-3-540-89435-3
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L. Grüne, W. Semmler, C. Öhrlein: Dynamic consumption and portfolio decisions with time varying asset returns
The Journal of Wealth Management 12 (2), 21 - 47, 2009

DOI: 10.3905/JWM.2009.12.2.021

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J. Pannek: Horizon Adaptation for Nonlinear Model Predictive Controllers with guaranteed Degree of Suboptimality
Preprint, University of Bayreuth, 2009, 20 pages

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J. Pannek: Receding Horizon Control: A Suboptimality-based Approach
Dissertation, Chair of Applied Mathematics, University of Bayreuth, Germany, 2009

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Publikationen 2008

R. Baier: Generalized Steiner Selections Applied to Standard Problems of Set-Valued Numerical Analysis
in: Differential Equations, Chaos and Variational Problems. Conference ``View on ODEs'' in Aveiro, Portugal, June 2006 (VODE 2006), V. Staicu (ed.)
Progress in Nonlinear Differential Equations and Their Application 75, Birkhäuser, Basel, 2008, 49 - 60

DOI: 10.1007/978-3-7643-8482-1_4
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R. Baier, E. Farkhi: The Directed Subdifferential of DC functions
19 pages, University of Bonn, June 2008

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R. Baier, F. Lempio: Von Eudoxos bis zur Klimafolgenforschung
Exhaustion, Finite Elemente und mengenwertige Numerik
in: Spektrum 1/08 (Jahr der Mathematik), H. Ruppert,
Holtz Druck, University of Bayreuth, Neudrossenfeld-Bayreuth, Germany, 2008, 6 - 12

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R. Baier, G. Perria: Hermite Interpolation with Directed Sets
University of Bonn, December 2008

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L. Grüne: Input-to-state stability, numerical dynamics and sampled-data control
GAMM-Mitteilungen 31, 94 - 114, 2008

DOI: 10.1002/gamm.200890005
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L. Grüne: Optimization based stabilization of nonlinear control systems
in: Proceedings of the Large-Scale Scientific Computations (LSSC07) in Sozopol, Bulgaria, I. Lirkov, S. Margenov, J. Wasniewski (eds.)
Lecture Notes in Computer Science 4818, Springer Verlag, 2008, 52 - 65

DOI: 10.1007/978-3-540-78827-0_5
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L. Grüne, F. Camilli, F. Wirth: Control Lyapunov Functions and Zubov's Method
SIAM Journal on Control and Optimization 47, 301 - 326, 2008

DOI: 10.1137/06065129X
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L. Grüne, O. Junge: Global optimal control of perturbed systems
Journal of Optimization Theory and Applications (JOTA) 136, 411 - 429, 2008

DOI: 10.1007/s10957-007-9312-z
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L. Grüne, F. Müller: Set oriented optimal control using past information
in: Proceedings of the 18th International Symposium on Mathematical Theory of Networks and Systems (MTNS2008), CD-Rom, Paper 125.pdf, 6 pages, Blacksburg, Virginia, 2008,

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L. Grüne, D. Nesic, J. Pannek, K. Worthmann: Redesign techniques for nonlinear sampled-data systems
at-Automatisierungstechnik 56 (Special Issue on Digitally Networked Systems), 38 - 48, 2008

DOI: 10.1524/auto.2008.0684
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L. Grüne, J. Pannek: Trajectory based suboptimality estimates for receding horizon controllers
in: Proceedings of the 18th International Symposium on Mathematical Theory of Networks and Systems (MTNS2008), CD-Rom, Paper 023.pdf, 6 pages, Blacksburg, Virginia, 2008,

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L. Grüne, A. Rantzer: On the infinite horizon performance of receding horizon controllers
IEEE Transactions on Automatic Control 53, 2100 - 2111, 2008

DOI: 10.1109/TAC.2008.927799
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L. Grüne, W. Semmler: Asset Pricing with Loss Aversion
Journal of Economic Dynamics and Control 32, 3253 - 3274, 2008

DOI: 10.1016/j.jedc.2008.01.002
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L. Grüne, K. Worthmann: Nonlinear sampled-data redesign: analytical formulas and their practical implementation
in: Proceedings of the 18th International Symposium on Mathematical Theory of Networks and Systems (MTNS2008), CD-Rom, Paper 084.pdf, 6 pages, Blacksburg, Virginia, 2008,

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L. Grüne, K. Worthmann: Sampled-data redesign for nonlinear multi-input systems
in: Geometric Control and Nonsmooth Analysis, F. Ancona, A. Bressan, P. Cannarsa, F. Clarke, P. R. Wolenski (eds.)
World Scientific, Singapore, 2008, 206 - 227

DOI: 10.1142/9789812776075_0011
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L. Grüne, K. Worthmann, D. Nesic: Continuous-time controller redesign for digital implementation: a trajectory based approach
Automatica 44, 225 - 232, 2008

DOI: 10.1016/j.automatica.2007.05.003
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Publikationen 2007

N. Altmüller: Poiseuille- und Quetschströmungen zwischen gewellten Platten
Diplomarbeit, Chair of Applied Mathematics, University of Bayreuth, Germany, July 2007

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R. Baier, C. Büskens, I. A. Chahma, M. Gerdts: Approximation of Reachable Sets by Direct Solution Methods of Optimal Control Problems
Optimization Methods and Software 22 (3), 433 - 452, 2007

DOI: 10.1080/10556780600604999
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R. Baier, I.A.Chahma, F. Lempio: Stability and Convergence of Euler's Method for State-Constrained Differential Inclusions
SIAM Journal on Optimization 18 (3; special issue on ``Variational Analysis and Optimization''), 1004 - 1026, 2007

DOI: 10.1137/060661867
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R. Baier, E. Farkhi: Regularity and Integration of Set-Valued Maps Represented by Generalized Steiner Points
Set-Valued Analysis 15 (2), 185 - 207, 2007

DOI: 10.1007/s11228-006-0038-0
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S. Becker,L. Grüne, W. Semmler: Comparing Accuracy of Second Order Approximation and Dynamic Programming
Computational Economics 30, 65 - 91, 2007

DOI: 10.1007/s10614-007-9087-1
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L. Grüne: Computing minimal optimization horizons for stabilizing unconstrained MPC schemes
in: Proceedings of the 6th International Congress on Industrial and Applied Mathematics (ICIAM 07) and GAMM Annual Meeting, Zürich, Switzerland, 2007, 4130007 - 4130008

DOI: 10.1002/pamm.200700203
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L. Grüne: Computing stability and performance bounds for unconstrained NMPC schemes
in: Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, Louisiana, 2007, 93 - 1268

DOI: 10.1109/CDC.2007.4434156
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L. Grüne, O. Junge: An efficient algorithm for perturbed shortest path problems
in: Proceedings of the 6th International Congress on Industrial and Applied Mathematics (ICIAM 07) and GAMM Annual Meeting, Zürich, Switzerland, 2007, 1025003 - 1025004

DOI: 10.1002/pamm.200700714
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L. Grüne, O. Junge: Approximately optimal nonlinear stabilization with preservation of the Lyapunov function property
in: Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, Louisiana, 2007, 702 - 707

DOI: 10.1109/CDC.2007.4434428
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L. Grüne, P.E. Kloeden, S. Siegmund, F. Wirth: Lyapunov's second method for nonautonomous differential equations
Discrete and Continuous Dynamical Systems - Series A 18 (Special Issue on Nonautonomous, Stochastic and Hamiltonian Dynamical Systems), 375 - 403, 2007

DOI: 10.3934/dcds.2007.18.375
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L. Grüne, D. Nesic, J. Pannek: Model predictive control for nonlinear sampled-data systems
in: Assessment and Future Directions of Nonlinear Model Predictive Control (NMPC05), F. Allgöwer, L. Biegler, R. Findeisen (eds.)
Lecture Notes in Control and Information Sciences 358, Springer Verlag, Heidelberg, 2007, 105 - 113

DOI: 10.1007/978-3-540-72699-9
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L. Grüne, W. Semmler: Asset Pricing with Dynamic Programming
Computational Economics 29, 233 - 265, 2007

DOI: 10.1007/s10614-006-9063-1
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L. Grüne, W. Semmler, L. Bernard: Firm value, diversified capital assets, and credit risk: towards a theory of default correlation
Journal of Credit Risk 3, 81 - 109, 2007/08

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G. Perria: Set-Valued Interpolation
Bayreuther Mathematische Schriften 79, vi + 154 pp., in: Bayreuth, Germany, 2007

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M. von Lossow: A min-max version of Dijkstra's algorithm with application to perturbed optimal control problems
in: Proceedings of the 6th International Congress on Industrial and Applied Mathematics (ICIAM07) and GAMM Annual Meeting, Zürich, Switzerland, 2007/08, 4130027 - 4130028

DOI: 10.1002/pamm.200700646
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Publikationen 2006

M. Gerdts: Optimal Control of Ordinary Differential Equations and Differential-Algebraic Equations
Habilitation, iv + 235 pages, Department of Mathematics, University of Bayreuth,
Bayreuth, Germany, 2006

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L. Grüne, F. Bauer, W. Semmler: Adaptive spline interpolation for Hamilton-Jacobi-Bellman equations
Applied Numerical Mathematics 56, 1196 - 1210, 2006

DOI: 10.1016/j.apnum.2006.03.011
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L. Grüne, F. Camilli, A. Cesaroni, F. Wirth: Stabilization of controlled diffusions via Zubov's method
Stochastics & Dynamics 6, 373 - 394, 2006

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L. Grüne, O. Junge: Optimal stabilization of hybrid systems using a set oriented approach
in: Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS2006), Kyoto, Japan, 2006, 2089 - 2093

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L. Grüne, P. E. Kloeden: Higher order numerical approximation of switching systems
Systems & Control Letters 55, 746 - 754, 2006

DOI: 10.1016/j.sysconle.2006.03.002
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L. Grüne, D. Nesic: A receding horizon control approach to sampled-data implementation of continuous-time controllers
Systems & Control Letters 55, 660 - 672, 2006

DOI: 10.1016/j.sysconle.2005.09.013
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L. Grüne, D. Nesic, K. Worthmann: High order approximations by sampled-data feedback
in: Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS2006), Kyoto, Japan, 2006, 1780 - 1787

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L. Grüne, A. Ratzer: Suboptimality estimates for receding horizon controllers
in: Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS2006), Kyoto, Japan, 2006, 120 - 127

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L. Grüne, P. Saint-Pierre: An invariance kernel representation of ISDS Lyapunov functions
Systems & Control Letters 55, 736 - 745, 2006

DOI: 10.1016/j.sysconle.2006.02.003
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G. Perria: Set Valued Interpolation
Dissertation, xvi + 119 S., Bayreuth, Germany, June 2006

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K. Worthmann: Digitale Implementierung kontinuierlicher Regler: Analyse und Optimierung
Diplomarbeit, Chair of Applied Mathematics, University of Bayreuth, Germany, 2006

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Publikationen 2005

R. Baier: Selection Strategies for Set-Valued Runge-Kutta Methods
in: Proceedings of the Numerical Analysis and Its Applications (NAA 2004), Third International Conference, Rousse, Bulgaria, June 29 - July 3, 2004, Revised Selected Papers, Z. Li, L.G. Vulkov, J. Wasniewski (eds.)
Lecture Notes in Computer Science 3401, Springer Verlag, Berlin-Heidelberg, 2005, 149 - 157

DOI: 10.1007/b106395
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R. Baier, M. Gerdts: Set-Valued Numerical Analysis and Optimal Control
in: Lecture Notes for the DAAD Intensive Course ``Optimization - Theory and Applications'' (July 05 -17, 2005), 264 pages, July 2005

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F. Camilli, L. Grüne, F. Wirth: Calculating the domain of attraction: Zubov's method and extensions
in: Proceedings of the Stability and Control Processes Conference (SCP 2005), dedicated to the 75th birthday anniversary of V. I. Zubov, Saint Petersburg, Russia, 2005, 27 - 36

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F. Camilli, L. Grüne, F. Wirth: Zubov's method for stochastic control systems
in: Proceedings of the 16th IFAC World Congress, DVD-ROM, Paper No. Mo-M20-TO/4, Prague, Czech Republic, 2005,

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T. Graf: Satellitentransfer von einem Geotransferorbit in einen geostationären Orbit
in: Dissertation, xiv + 158 pp., Bayreuth, Germany, 2005

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L. Grüne, O. Junge: A set oriented approach to optimal feedback stabilization
Systems & Control Letters 54, 169 - 180, 2005

DOI: 10.1016/j.sysconle.2004.08.005
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L. Grüne, O. Junge: Constructing robust feedback laws by set oriented numerical methods
in: Proceedings of the GAMM Annual Meeting, Luxembourg, 2005, 157 - 162

DOI: 10.1002/pamm.200510059
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L. Grüne, M. Kato, W. Semmler: Solving ecological management problems using dynamic programming
Journal of Economic Behavior & Organization 57, 448 - 473, 2005

DOI: 10.1016/j.jebo.2005.04.002
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L. Grüne, D. Nesic: Lyapunov based continuous-time nonlinear controller redesign for sampled-data implementation
Automatica 41, 1143 - 1156, 2005

DOI: 10.1016/j.automatica.2005.03.001
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L. Grüne, D. Nesic: Nonlinear sampled-data controller redesign via Lyapunov functions
in: Proceedings of the 16th IFAC World Congress, DVD-ROM, Paper No. Fr-A17-TO/5, Prague, Czech Republic, 2005,

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L. Grüne, D. Nesic, J. Pannek: Model predictive sampled-data redesign for nonlinear systems
in: Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference (ECC2005), Sevilla, Spain, 2005, 36 - 41

DOI: 10.1109/CDC.2005.1582127
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L. Grüne, D. Nesic, J. Pannek: Redesign techniques for nonlinear sampled-data control
in: Oberwolfach Reports 11, 2005, 584 - 586

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L. Grüne, P. Saint-Pierre: A set valued characterization of ISDS Lyapunov functions
in: Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference (ECC2005), Sevilla, Spain, 2005, 4718 - 4723

DOI: 10.1109/CDC.2005.1582907
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L. Grüne, W. Semmler: Default risk, asset pricing and debt control
Journal of Financial Econometrics 3, 79 - 106, 2005

DOI: 10.1093/jjfinec/nbi006
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L. Grüne, W. Semmler, M. Sieveking: Creditworthyness and thresholds in a credit market model with multiple equilibria
Economic Theory 25, 287 - 315, 2005

DOI: 10.1007/s00199-003-0442-8
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J. Pannek: Modellprädiktive Regelung nichtlinearer sampled-data Systeme
Diplomarbeit, Chair of Applied Mathematics, University of Bayreuth, Germany, March 2005

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G. Perria: SVUPI: Set Valued Univariate Polynomial Interpolation. White Paper for the SVUPI C++ class package
in: White Paper, Bayreuth, Germany, 2005

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M. von Lossow: Mengenorientierte optimale Steuerung und Fehlerschätzung
Diplomarbeit, Chair of Applied Mathematics, University of Bayreuth, Germany, November 2005

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Publikationen 2004

R. Baier: Convergence Analysis for Selection Strategies of Set-Valued Runge-Kutta Methods
Technical Report, 40 pages, University of Bayreuth, Bayreuth, Germany, June 2004

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R. Baier, N. Dyn: Rotational Metric Average in |R^n
Technical Report, 11 pages, University of Bayreuth, Bayreuth, Germany, 2004

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F. Camilli, L. Grüne, F. Wirth: Characterizing controllability probabilities of stochastic control systems via Zubov's method
in: Proceedings of the 16th International Symposium on Mathematical Theory of Networks and Systems (MTNS2004), CD-ROM, WA3, Paper No. 65, Leuven, Belgium, 2004,

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F. Camilli, L. Grüne, F. Wirth: Construction of Lyapunov functions on the domain of asymptotic nullcontrollability: numerics
in: Proceedings of NOLCOS 2004, Stuttgart, Germany, 2004, 883 - 888

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F. Camilli, L. Grüne, F. Wirth: Construction of Lyapunov functions on the domain of asymptotic nullcontrollability: theory
in: Proceedings of NOLCOS 2004, Stuttgart, Germany, 2004, 877 - 882

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L. Grüne: Error estimation and adaptive discretization for the discrete stochastic Hamilton-Jacobi-Bellman equation
Numerische Mathematik 99, 85 - 112, 2004

DOI: 10.1007/s00211-004-0555-4
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L. Grüne: Quantitative aspects of the input-to-state stability property
in: Optimal Control, Stabilization, and Nonsmooth Analysis (MCT03), M. de Queiroz, M. Malisoff, P.Wolenski (eds.)
Lecture Notes in Control and Information Sciences 301, Springer Verlag, Heidelberg, 2004, 215 - 230

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L. Grüne: Robust asymptotic controllability under time-varying perturbations
Stochastics & Dynamics 4, 297 - 316, 2004

DOI: 10.1142/S0219493704001085
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L. Grüne, W. Semmler: Using dynamic programming with adaptive grid scheme for optimal control problems in economics
Journal of Economic Dynamics and Control 28 (12), 2427 - 2456, 2004

DOI: 10.1016/j.jedc.2003.11.002
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Publikationen 2003

I. A. Chahma: Set-Valued Discrete Approximations of State-Constrained Differential Inclusions
Dissertation, iv + 125 pp., Bayreuth, Germany, January 2003

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I. A. Chahma: Set-Valued Discrete Approximation of State-Constrained Differential Inclusions
Bayreuther Mathematische Schriften 67, 3 - 161, in: Bayreuth, Germany, 2003

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L. Grüne: Attraction rates, robustness and discretization of attractors
SIAM Journal on Numerical Analysis 41, 2096 - 2113, 2003

DOI: 10.1137/S003614290139411X
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L. Grüne, F. Camilli: Characterizing attraction probabilities via the stochastic Zubov equation
Discrete and Continuous Dynamical Systems - Series B 3, 457 - 468, 2003

DOI: 10.3934/dcdsb.2003.3.457
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L. Grüne, P. E. Kloeden: Numerical schemes of higher order for a class of nonlinear control systems
in: Numerical Methods and Applications, I. Dimov, I. Lirkov, S. Margenov, Z. Zlatev (eds.)
Springer Lecture Notes in Computer Science 2542, Borovets, Bulgaria, 2003, 213 - 220

DOI: 10.1007/3-540-36487-0
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L. Grüne, D. Nesic: Optimization based stabilization of sampled-data nonlinear systems via their approximate discrete-time models
SIAM Journal on Control and Optimization 42, 98 - 122, 2003

DOI: 10.1137/S036301290240258X
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G. Perria: Gerichtete Polytope: Arithmetische Operationen und Visualisierung mittels CGAL.
Diplomarbeit, xxvi + 161 pp., Bayreuth, Germany, February 2003

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Publikationen 2002

R. Baier, N. Dyn, E. Farkhi: The metric average of 1D Compact sets
in: Approximation Theory X: Volume 1. Abstract and Classical Analysis, C. K. Chui, L. L. Schumaker, J. Stöckler (eds.)
Innovations in Applied Mathematics, Vanderbuilt University Press, Nashville, TN, 2002, 9 - 22

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R. Baier, F. Lempio, E. Polovinkin: Set-Valued Integration with Negative Weights
Technical Report, 35 pages, University of Bayreuth, Bayreuth, Germany, 2002

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F. Camilli, L. Grüne, F. Wirth: A generalization of Zubov's method to perturbed systems
in: Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, Nevada, 2002, 3518 - 3523

DOI: 10.1109/CDC.2002.1184420
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F. Colonius, L. Grüne (eds.): Dynamics, Bifurcations and Control (NCN)
in: Lecture Notes in Control and Information Sciences 273, Springer Verlag, 2002, xi + 303 pages

DOI: 10.1007/3-540-45606-6
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S. Cyganowski, L. Grüne, P. E. Kloeden: MAPLE for Jump-Diffusion Stochastic Differential Equations in Finance
in: Programming Languages and Systems in Computational Economics and Finance, S.S. Nielsen (ed.)
Kluwer Academic Publishers, Dordrecht, 2002, 441 - 460

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T. Fischer: Über Modellierung, Analysis und Simulation von Stofftransport auf Wurzeln in strukturierten Böden
Dissertation, 153 pp., Department of Mathematics, University of Technology in Darmstadt,
Darmstadt, Germany, 2002

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K. Chudej, Ch. Büskens, T. Graf: Solution of a Hard Flight Path Optimization Problem by Different Optimization Codes High-Performance Scientific and Engineering Computing
in: High Performance Scientific and Engineering Computing, M. Breuer, F. Durst, Ch. Zenger (eds.)
Lecture Notes in Control and Information Sciences 21, Springer, Berlin-Heidelberg, 2002, 289 - 296

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L. Grüne: Asymptotic Behavior of Dynamical and Control Systems under Perturbation and Discretization
in: Lecture Notes in Mathematics 1783, Springer Verlag, 2002,

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L. Grüne: Gain preserving Lyapunov functions for perturbed and controlled systems
in: Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, Nevada, 2002, 707 - 712

DOI: 10.1109/CDC.2002.1184587
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L. Grüne: Input-to-state dynamical stability and its Lyapunov function characterization
IEEE Transactions on Automatic Control 47, 1499 - 1504, 2002

DOI: 10.1109/TAC.2002.802761
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L. Grüne: Quantitative aspects of the input-to-state stability property
in: Proceedings of the Mathematical Theory of Networks and Systems (MTNS2002), CD-Rom, Article TUA4-4, South Bend, Indiana, 2002,

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L. Grüne, D. Nesic: Stabilization of sampled-data nonlinear systems via their approximate models: an optimization based approach
in: Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, Nevada, 2002, 1934 - 1939

DOI: 10.1109/CDC.2002.1184810
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N. P. Osmolovskii, F. Lempio: Transformation of quadratic forms to perfect squares for broken extremals
Set-Valued Analysis 10 (2-3), 209 - 232, 2002

DOI: 10.1023/A:1016588116615

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Publikationen 2001

R. Baier, E. Farkhi: Differences of Convex Compact Sets in the Space of Directed Sets, Part I: The Space of Directed Sets
Set-Valued Analysis 9 (3), 217 - 245, 2001

DOI: 10.1023/A:1012046027626
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R. Baier, E. Farkhi: Differences of Convex Compact Sets in the Space of Directed Sets, Part II: Visualization of Directed Sets
Set-Valued Analysis 9 (3), 247 - 272, 2001

DOI: 10.1023/A:1012009529492
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R. Baier, E. Farkhi: Directed Derivatives of Convex Compact-Valued Mappings
in: Proceedings of the Conference "Advances in Convex Analysis and Global Optimization: Honoring the Memory of C. Caratheodory (1873-1950)" held at Pythagorion, Samos, Greece in June 5-9, 2000, N. Hadjisavvas, P. M. Pardalos (eds.)
Nonconvex Optimization and Its Applications 54, Kluwer Academic Publishers, Dordrecht-Boston-London, 2001, 501 - 514

DOI: 10.1007/978-1-4613-0279-7_32
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S. Cyganowski, L. Grüne, P. E. Kloeden: MAPLE for Stochastic Differential Equations
in: Theory and Numerics of Differential Equations, J.F. Blowey, J.P. Coleman, A.W. Craig (eds.)
Springer Verlag, 2001, 127 - 178

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T. Fischer, G. Leugering: On instantaneous control of singularly perturbed hyperbolic equations on graphs
in: Partial differential equations on multistructures, F. A. Mehmeti, J. von Below and S. Nicaise (eds.)
Lecture Notes in Pure and Applied Mathematics 219, Marcel Dekker, Inc., New York, 2001, 69 - 97

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M. Gerdts: Numerische Methoden optimaler Steuerprozesse mit differential-algebraischen Gleichungssystemen höheren Indexes und ihre Anwendungen in der Kraftfahrzeugsimulation und Mechanik
in: Dissertation, iv + 139 pp., Bayreuth, Germany, 2001

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L. Grüne: Adaptive grid generation for evolutive Hamilton-Jacobi-Bellman equations
in: Numerical Methods for Viscosity Solutions and Applications, M. Falcone, Ch. Makridakis (eds.)
World Scientific, Singapore, 2001, 153 - 172

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L. Grüne: Asymptotic Behavior of Dynamical and Control Systems under Perturbation and Discretization
Habilitation, J.W. Goethe-Universität Frankfurt, 2001

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L. Grüne: Persistence of attractors for one-step discretizations of ordinary differential equations
IMA Journal of Numerical Analysis 21, 751 - 767, 2001

DOI: 10.1093/imanum/21.3.751
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L. Grüne: Subdivision techniques for the computation of domains of attraction and reachable sets
in: Proceedings of NOLCOS 2001, St. Petersburg, Russia, 2001, 762 - 767

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L. Grüne, F. Camilli, F. Wirth: A generalization of Zubov's method to perturbed systems
SIAM Journal on Control and Optimization 40, 496 - 515, 2001

DOI: 10.1137/S036301299936316X
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L. Grüne, P. E. Kloeden: Discretization, inflation and perturbation of attractors
in: Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems (DANSE), B. Fiedler (ed.)
Springer Verlag, 2001, 399 - 416

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L. Grüne, P. E. Kloeden: Higher order numerical schemes for affinely controlled nonlinear systems
Numerische Mathematik 89, 669 - 690, 2001

DOI: 10.1007/s002110000279
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L. Grüne, P. E. Kloeden: Pathwise Approximation of Random Ordinary Differential Equations
BIT - Numerical Mathematics 41, 710 - 721, 2001

DOI: 10.1023/A:1021995918864
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F. Lempio: Über Nützliches und Schönes in der Mathematik
Mathematikinformation 35, 3 - 18, 2001

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G. Leugering, W. Rathmann: On modeling, analysis and simulation of optimal control problems for dynamic networks of Euler-Bernoulli and Rayleigh-beams
in: Control of nonlinear distributed parameter systems, Goong Chen, I. Lasiecka and Jianxin Zhou (eds.)
Lecture Notes in Pure and Applied Mathematics 218, Dekker, New York, 2001, 199 - 232

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Publikationen 2000

F. Camilli, L. Grüne, F. Wirth: A regularization of Zubov's equation for robust domains of attraction
in: Nonlinear Control in the Year 2000 Volume 1 (NCN), A. Isidori, F. Lamnabhi-Lagarrigue, W. Respondek (eds.)
Lecture Notes in Control and Information Sciences 258, Springer Verlag, London, 2000, 277 - 290

DOI: 10.1007/BFb0110202
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M. Falcone, L. Grüne, F. Wirth: A maximum time approach to the computation of robust domains of attraction
in: EQUADIFF 99, Berlin, B. Fiedler, K. Gröger, J. Sprekels (eds.)
World Scientific, Singapore, 2000, 844 - 849

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L. Grüne: A uniform exponential spectrum for linear flows on vector bundles
Journal of Dynamics and Differential Equations 12, 435 - 448, 2000

DOI: 10.1023/A:1009024610394
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L. Grüne: Attractors under perturbation and discretization
in: Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, 2000, 2118 - 2122

DOI: 10.1109/CDC.2000.914107
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L. Grüne: Computation of the Lyapunov Spectrum
in: F. Colonius, W. Kliemann, The Dynamics of Control, Appendix D, Birkhäuser, 2000, 569 - 596

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L. Grüne: Convergence Rates of Perturbed Attracting Sets with Vanishing Perturbations
Journal of Mathematical Analysis and Applications 244, 369 - 392, 2000

DOI: 10.1006/jmaa.2000.6707
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L. Grüne: Homogeneous state feedback stabilization of homogeneous systems
in: Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, 2000, 3409 - 3414

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L. Grüne: Homogeneous state feedback stabilization of homogeneous systems
SIAM Journal on Control and Optimization 38, 1288 - 1214, 2000

DOI: 10.1137/S0363012998349303
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L. Grüne, F. Camilli: Numerical approximation of the maximal solutions for a class of degenerate Hamilton-Jacobi equations
SIAM Journal on Numerical Analysis 38, 1540 - 1560, 2000

DOI: 10.1137/S003614299834798X
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L. Grüne, F. Camilli, F. Wirth: Homogeneous control Lyapunov functions for homogeneous control systems
in: Proceedings of the Mathematical Theory of Networks and Systems (MTNS2000), CD-Rom, Article B99, Perpignan, 2000,

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L. Grüne, F. Camilli, F. Wirth: Zubov's method for perturbed differential equations
in: Proceedings of the Mathematical Theory of Networks and Systems (MTNS2000), CD-Rom, Article B100, Perpignan, 2000,

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L. Grüne, E. Sontag, F. Wirth: On equivalence of exponential and asymptotic stability under changes of variables
in: EQUADIFF 99, Berlin, B. Fiedler, K. Gröger, J. Sprekels (eds.)
World Scientific, Singapore, 2000, 850 - 852

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L. Grüne, F. Wirth: Computing control Lyapunov functions via a Zubov type algorithm
in: Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, 2000, 2129 - 2134

DOI: 10.1109/CDC.2000.914109
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L. Grüne, F . Wirth: On the rate of convergence of infinite horizon discounted optimal value functions
Nonlinear Analysis: Real World Applications 1, 499 - 515, 2000

DOI: 10.1016/S0362-546X(99)00288-6
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F. Lempio: Finite element methods - from ancient to modern times (in Bulgarian)
in: Proceedings of Twenty Ninth Spring Conference of the Union of Bulgarian Mathematicians, Lovetch, April 3-6, 2000, Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences (ed.)
2000, 5 - 17

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N. P. Osmolovskii, F. Lempio: Jacobi conditions and Riccati equation for broken extremal
Journal of Mathematical Sciences 100 (5), 2572 - 2592, 2000

DOI: 10.1007/BF02673843

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W. Rathmann: Modellierung, Simulation und Steuerung von Netzwerken schwingender Balken mittels dynamischer Bereichszerlegung
in: Dissertation, xvii + 202 pp., Bayreuth, Germany, 2000

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Publikationen 1999

R. Baier, E. Farkhi: Directed Sets and Differences of Convex Compact Sets
in: Systems modelling and optimization, Proceedings of the 18th IFIP TC7 Conference held in Detroit, Michigan, July 22-25, 1997, P. M. Polis, A. L. Dontchev, P. Kall, I. Lasiecka, A. W. Olbrot (eds.)
Research Notes in Mathematics, Chapman and Hall/CRC, Boca Raton-London-New York-Washington, D.C., 1999, 135 - 143

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M. Dellnitz: Verzweigungsphänomene
in: Department of Mathematics, University of Bayreuth (eds.)
Bayreuther Mathematische Schriften 56, Bayreuth, Germany, 1999, 43 - 58

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L. Grüne: Input-to-state stability of exponentially stabilized semilinear control systems with inhomogeneous perturbations
Systems & Control Letters 38, 27 - 35, 1999

DOI: 10.1016/S0167-6911(99)00044-4
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L. Grüne: Stabilization by sampled and discrete feedback with positive sampling rate
in: Stability and Stabilization of Nonlinear Systems (NCN), Chapter 9, D. Aeyels, F. Lamnabhi-Lagarrigue, A. van der Schaft (eds.)
Lecture Notes in Control and Information Sciences 246, Springer Verlag, London, 1999, 165 - 182

DOI: 10.1007/1-84628-577-1
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L. Grüne, M . Metscher, M. Ohlberger: On Numerical Algorithm and Interactive Visualization for Optimal Control Problems
Computing and Visualization in Science 1 (4), 221 - 229, 1999

DOI: 10.1007/s007910050020
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L. Grüne, E. Sontag, F. Wirth: Asymptotic stability equals exponential stability, and ISS equals finite energy gain - if you twist your eyes
Systems & Control Letters 38, 127 - 134, 1999

DOI: 10.1016/S0167-6911(99)00053-5
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L. Grüne, E. Sontag, F. Wirth: On the equivalence between asymptotic and exponential stability, and between ISS and finite H-infinity gain
in: Proceedings of the 38th IEEE Conference on Decision and Control, Phoenix, Arizona, 1999, 1220 - 1225

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L. Grüne, F. Wirth: Feedback stabilization of discrete-time homogeneous semi-linear systems
Systems & Control Letters 37, 19 - 30, 1999

DOI: 10.1016/S0167-6911(98)00110-8
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F. Lempio: Über zwei Jahrtausende Finite Elemente - Von Eudoxos bis zur Hyperthermietherapie
in: Department of Mathematics, University of Bayreuth (eds.)
Bayreuther Mathematische Schriften 56, Bayreuth, Germany, 1999, 59 - 78

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N. P. Osmolovskii, F. Lempio: Jacobi conditions and Riccati equation for broken extremal
in: Proceedings of the International Conference Dedicated to 90th Anniversary of L.S.Pontryagin, August 31-September 6, 1998, Moscow, R. V. Gamkrelidze,
1999, 187 - 215

DOI: 10.1007/BF02673843

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Publikationen 1998

F. Camilli, L. Grüne: Maximal solutions for a class of singular Hamilton-Jacobi equations
in: Proceedings of the Mathematical Theory of Networks and Systems (MTNS98), Padova, 1998, 447 - 450

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L. Grüne, F. Wirth: On linear convergence of discounted optimal control problems with vanishing discount rate
in: Proceedings of the Mathematical Theory of Networks and Systems (MTNS98), Padova, 1998, 185 - 188

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L. Grüne: Asymptotic Controllability and Exponential Stabilization of Nonlinear Control Systems at Singular Points
SIAM Journal on Control and Optimization 36, 1585 - 1603, 1998

DOI: 10.1137/S0363012997315919
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L. Grüne: Numerical stabilization at singular points
in: Proceedings of the Mathematical Theory of Networks and Systems (MTNS98), Padova, 1998, 633 - 636

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L. Grüne: On input-to-state stabilizability of semilinear control systems
in: Proceedings of the Mathematical Theory of Networks and Systems (MTNS98), Padova, 1998, 181 - 184

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L. Grüne: On the relation between discounted and average optimal control problems
Journal of Differential Equations 148, 65 - 99, 1998

DOI: 10.1006/jdeq.1998.3451
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L. Grüne, F. Wirth: Stabilization of discrete-time bilinear systems
in: Proceedings of the GAMM Jahrestagung 1997, ZAMM, Supplement 3, Regensburg, 1998, 925 - 926

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F. Lempio: Numerische Mathematik II: Methoden der Analysis
in: Bayreuther Mathematische Schriften 55, Bayreuth, Germany, 1998, vi + 263 pp.

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F. Lempio: Über zwei Jahrtausende Finite Elemente - Von Eudoxos bis zur Hyperthermietherapie
in: 27. Kolloquium Mathematik-Didaktik der Universität Bayreuth, 18. Febr. 1998, Department of Mathematics, University of Bayreuth (eds.)
Bayreuth, Germany, 1998, 3 - 18

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F. Lempio, V. M. Veliov: Discrete approximations of differential inclusions
in: Department of Mathematics, University of Bayreuth (eds.)
Bayreuther Mathematische Schriften 54, Bayreuth, Germany, 1998, 149 - 232

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F. Lempio, V. M. Veliov: Discrete approximations of differential inclusions
GAMM-Mitteilungen 21 (2), 103 - 135, 1998

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N. P. Osmolovskii, F. Lempio: Jacobi conditions and Riccati equation for broken extremal (in Russian)
in: Proceedings of the International Conference Dedicated to 90th Anniversary of L. S. Pontryagin, August, 31 - September, 6, 1998, Moscow. Volume 1: Optimal Control, R. V. Gamkrelidze (ed.)
Modern Mathematics and its Applications 60, VINITI, 1998, 187 - 215

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Publikationen 1997

L. Grüne: A Spectral Condition for Asymptotic Controllability and Stabilization at Singular Points
in: Proceedings of the 36th IEEE Conference on Decision and Control in San Diego, US, California, 1997, 4431 - 4435

DOI: 10.1109/CDC.1997.649648
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L. Grüne: An Adaptive Grid Scheme for the discrete Hamilton-Jacobi-Bellman Equation
Numerische Mathematik 75, 319 - 337, 1997

DOI: 10.1007/s002110050241
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L. Grüne: Discrete Feedback Stabilization of Nonlinear Control Systems at a Singular Point
in: Proceedings of the European Control Conference (ECC) 1997, CD-Rom, Paper No. 806, Brussels, 1997,

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F. Lempio: Numerische Mathematik I: Methoden der Linearen Algebra
in: Bayreuther Mathematische Schriften 51, Bayreuth, Germany, 1997, vi + 234 pp.

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F. Lempio, D. Silin: Generalized differential equations with strongly one-sided Lipschitzian right-hand side
Differential Equations 32 (11), 1485 - 1491, 1997

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Publikationen 1996

L. Grüne: Discrete Feedback Stabilization of Semilinear Control Systems
ESAIM: Control, Optimisation and Calculus of Variations 1, 207 - 224, 1996

DOI: 10.1051/cocv:1996106
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L. Grüne: Numerical Stabilization of Bilinear Control Systems
SIAM Journal on Control and Optimization 34, 2024 - 2050, 1996

DOI: 10.1137/S0363012994272290
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L. Grüne: Numerische Berechnung des Lyapunov-Spektrums bilinearer Kontrollsysteme
Logos-Verlag, Berlin und Dissertation, Universität Augsburg. Ausgezeichnet mit dem Universitätspreis der Universität Augsburg, 1996,

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F. Lempio, D. Silin: Generalized differential equations with strongly one-sided Lipschitzian right-hand side
Differentsial’nye Uravneniya 32 (11), 1488 - 1494, 1996

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Publikationen 1995

R. Baier: Mengenwertige Integration und die diskrete Approximation erreichbarer Mengen
Bayreuther Mathematische Schriften 50, xxii+248 pp., 1995

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F. Lempio: Euler's Method Revisited
Proceedings of the Steklov Institute of Mathematics, Moscow 211, 429 - 449, Nauka, Moscow, Russia, 1995

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F. Lempio: Euler's Method Revisited
Trudy Mat. Inst. Steklov 211, 473 - 494, Nauka, Moscow, Russia, 1995

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F. Lempio: Set-valued interpolation, differential inclusions, and sensitivity in optimization
in: Recent Developments in Well-Posed Variational Problems, R. Lucchetti, J. Revalski (eds.)
Mathematics and Its Applications 331, Kluwer Academic Publishers, Dordrecht-Boston-London, 1995, 137 - 169

DOI: 10.1007/978-94-015-8472-2_6
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Publikationen 1994

R. Baier: Extrapolation Methods for the Computation of Set-Valued Integrals and Reachable Sets of Linear Differential Inclusions
ZAMM 74 (6), T555 - T557, 1994

DOI: 10.1002/zamm.19940740605

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R. Baier: Mengenwertige Integration und die diskrete Approximation erreichbarer Mengen
Dissertation, xix+202 pp., Department of Mathematics, University of Bayreuth, Germany, 1994

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R. Baier, F. Lempio: Approximating Reachable Sets by Extrapolation Methods
in: Curves and Surfaces in Geometric Design. Papers from the Second International Conference on Curves and Surfaces, held in Chamonix-Mont-Blanc, France, July 10-16, 1993, P. J. Laurent, A. Le Méhauteé, L. L. Schumaker (eds.)
A K Peters, Wellesley, 1994, 9 - 18

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R. Baier, F. Lempio: Computing Aumann's Integral
in: Modeling Techniques for Uncertain Systems,Proceedings of a Conference held in Sopron, Hungary, July 6-10, 1992, A. B. Kurzhanski, V. M. Veliov (eds.)
Progress in Systems and Control Theory 18, Birkhäuser, Basel, 1994, 71 - 92

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L. Grüne: Numerische optimale Steuerung und Stabilisierung
Diplomarbeit, University of Augsburg, 1994

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F. Lempio: Einführung in die Benutzung der Datenbanken MATH und CompactMATH
in: Technical Report, 2nd edition, Bayreuth, Germany, 1994

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Publikationen 1993

W. Achtziger: Optimierung von einfach und mehrfach belasteten Stabwerken
in: Dissertation, xviii + 353 pp., Bayreuth, Germany, 1993

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A. Kastner-Maresch, F. Lempio: Difference methods with selection strategies for differential inclusions
Numerical Functional Analysis and Optimization 14 (5 & 6), 555 - 572, 1993

DOI: 10.1080/01630569308816539

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F. Lempio: Modified Euler methods for differential inclusions
in: Set-Valued Analysis and Differential Inclusions. A Collection of Papers resulting from a Workshop held in Pamporovo, Bulgaria, September 17-21, 1990, A. B. Kurzhanski, V. M. Veliov (eds.)
Progr. Systems Control Theory 16, Birkhäuser Verlag, Boston-Basel-Berlin, 1993, 131 - 148

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Publikationen 1992

A. Dontchev, F. Lempio: Difference Methods for Differential Inclusions: A Survey
SIAM Review 34 (2), 263 - 294, 1992

DOI: 10.1137/1034050

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F. Lempio: Difference methods for differential inclusions
in: Modern Methods of Optimization. Proceedings of a Summer School at Thurnau (Germany), September 30-October 6, 1990, Lecture Notes in Economics and Mathematical Systems 378, Springer Verlag, Berlin-Heidelberg-New York, 1992, 236 - 273

DOI: 10.1007/978-3-662-02851-3_8

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Publikationen 1991

W. Alt: Stability of Solutions and the Lagrange-Newton Method for Nonlinear Optimization and Optimal Control Problems
Habilitation, Department of Mathematics, University of Bayreuth,
Bayreuth, Germany, 1991

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W. Alt: Parametric optimization with applications to optimal control and sequential quadratic programming
in: Department of Mathematics, University of Bayreuth (eds.)
Bayreuther Mathematische Schriften 35, Bayreuth, Germany, 1991, 1 - 37

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F. Lempio: The numerical treatment of differential inclusions
in: Proceedings of the International Conference on Differential Equations and Applications, held in Russe, Bulgaria, August 13--19, 1989, P. Popivanov, S. Tersian (eds.)
Technical University-Russe, Centre of Mathematics, Russe, Bulgaria, 1991, 353 - 364

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Publikationen 1990

R. Baier: Konvergenz und numerische Realisierung von Mehrgitterverfahren und Diskretisierungsmethoden für Randwertaufgaben zweiter Ordnung
Diplomarbeit, xix + 202pp., University of Bayreuth, July 1990

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A. Kastner-Maresch: Differenzenverfahren höherer Ordnung für Differentialinklusionen
Dissertation, 106 pp., Dissertations Druck Darmstadt, Bayreuth, Germany, 1990

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Publikationen 1989

H. Schramm: Eine Kombination von Bundle- und Trust-Region-Verfahren zur Lösung nichtdifferenzierbarer Optimierungsprobleme
in: Dissertation, viii +205 pp., Bayreuth, Germany, 1989

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Publikationen 1988

W. Alt, F. Lempio: Programmbibliothek des Lehrstuhls für Angewandte Mathematik der Universität Bayreuth
in: Manual, Bayreuth, Germany, 1988

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Publikationen 1985

K. Schilling: Simpliziale Algorithmen zur Berechnung von Fixpunkten mengenwertiger Operatoren
Dissertation, 191 pp., Department of Mathematics, University of Bayreuth,
Wissenschaftlicher Verlag Trier (WVT), Trier, Germany, 1985

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Publikationen 1982

F. Lempio, J. Zowe: Higher order optimality conditions
in: Modern applied mathematics (Bonn, 1979), North-Holland, Amsterdam, 1982, 147 - 193

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Publikationen 1981

U. Mackenroth: Optimalitätsbedingungen und Dualität für zustandsrestringierte konvexe parabolische Kontrollprobleme
Habilitation, Department of Mathematics, University of Bayreuth,
Bayreuth, Germany, 1981

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Publikationen 1980

F. Lempio, H. Maurer: Differential stability in infinite-dimensional nonlinear programming
Applied Mathematics and Optimization 6 (2), 139 - 152, 1980

DOI: 10.1007/BF01442889

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Publikationen 1979

W. Alt: Stabilität mengenwertiger Abbildungen mit Anwendungen auf nichtlineare Optimierungsprobleme
in: Dissertation, vii + 107 pp., Department of Mathematics, University of Bayreuth,
Bayreuth, Germany, 1979

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F. Lempio: Dualität und Stabilität
in: Numerical mathematics (Sympos., Inst. Appl. Math., Univ. Hamburg, Hamburg, 1979), Internat. Ser. Numer. Math. 49, Birkhäuser, Basel, 1979, 107 - 124

DOI: 10.1007/978-3-0348-6285-1_8

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Publikationen 1978

F. Lempio, H. Maurer: Differentiable perturbations of infinite optimization problems
in: Optimization and operations research (Proc. Workshop, Univ. Bonn, Bonn, 1977), Lecture Notes in Economics and Mathematical Systems 157, Springer, Berlin, 1978, 181 - 191

DOI: 10.1007/978-3-642-95322-4_19

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Publikationen 1976

F. Lempio: Minimumnormprobleme und zeitoptimale Steuerungen
in: Numerische Methoden der Approximationstheorie, Band 3 (Tagung, Math. Forschungsinst., Oberwolfach, 1975), Internat. Ser. Numer. Math. 30, Birkhäuser, Basel, 1976, 277 - 298

DOI: 10.1007/978-3-0348-7692-6_14

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Publikationen 1974

F. Lempio: Anwendungen der Lagrangeschen Multiplikatorenregel auf Approximations-, Variations- und Steuerungsprobleme
in: Numerische Methoden bei Differentialgleichungen und mit funktionalanalytischen Hilfsmitteln (Vortragsauszüge der Tagungen, Tech. Univ. Clausthal-Zellerfeld und Oberwolfach, 1972), Internat. Schr. Numer. Math. 19, Birkhäuser, Basel, 1974, 147 - 157

DOI: 10.1007/978-3-0348-6988-1_13

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F. Lempio: Bemerkungen zur Lagrangeschen Funktionaldifferentialgleichung
in: Numerische Methoden bei Differentialgleichungen und mit funktionalanalytischen Hilfsmitteln (Vortragsauszüge der Tagungen, Tech. Univ. Clausthal-Zellerfeld und Oberwolfach, 1972), Internat. Schr. Numer. Math. 19, Birkhäuser, Basel, 1974, 141 - 146

DOI: 10.1007/978-3-0348-6988-1_12

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F. Lempio: Zur optimalen Steuerung nichtlinearer Entwicklungen
in: Sechste Oberwolfach-Tagung über Operations Research (1973), Teil II, Operations Research Verfahren XIX, Hain, Meisenheim am Glan, 1974, 35 - 41

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Publikationen 1973

F. Lempio: Dualität und optimale Steuerungen
in: Numerische Methoden bei bei Optimierungsaufgaben (Tagung, Math. Forschungsinst., Oberwolfach, 1971), Internat. Schr. Numer. Math. 17, Birkhäuser, Basel, 1973, 101 - 109

DOI: 10.1007/978-3-0348-5971-4_9

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F. Lempio: Eine Verallgemeinerung des Satzes von Fritz John
in: V. Oberwolfach-Tagung über Operations Research, 13.-19. August 1972, Teil 2, R. Henn, H. P. Künzi, H. Schubert (eds.)
Operations Res.-Verf. 17, Verlag Anton Hain, Meisenheim am Glan, 1973, 239 - 247

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F. Lempio: Positive Lösungen unendlicher Gleichungs- und Ungleichungssysteme und Lagrange-Multiplikatoren für infinite differenzierbare Optimierungsprobleme
Zeitschrift für Angewandte Mathematik und Mechanik 53 (1), 61 - 62, T162, 1973

DOI: 10.1002/zamm.19730530108

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Publikationen 1972

F. Lempio: Differenzierbare Optimierung mit unendlich vielen Nebenbedingungen
in: IV. Oberwolfach-Tagung über Operations Research, 25.-31. Juli 1971, Teil 2, R. Henn, H. P. Künzi, H. Schubert (eds.)
Operations Res.-Verf. 13, Verlag Anton Hain, Meisenheim am Glan, 1972, 265 - 273

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F. Lempio: Tangentialmannigfaltigkeiten und infinite Optimierung
Habilitation, 73 pages, Institute of Applied Mathematics, University of Hamburg, Hamburg, Germany, 1972

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Publikationen 1971

F. Lempio: Lineare Optimierung in unendlichdimensionalen Vektorräumen
Computing (Arch. Elektron. Rechnen) 8, 284 - 290, 1971

DOI: 10.1007/BF02234110

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F. Lempio: Separation und Optimierung in linearen Räumen
Dissertation, 52 pages, Institute of Applied Mathematics, University of Hamburg, Hamburg, Germany, 1971

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