Set-valued numerical analysis

start of the project: 2008

funding institution:

until 2017: The Hermann Minkowski Center for Geometry in Tel Aviv, Israel;
DAAD; Bulgarian Academy of Sciences

PROJECT MEMBERS

principal investigator

AD Dr. Robert Baier

project members

Dr. Elza Farkhi

Dr. Gilbert Perria (project member until 09/2010  )

AIMS OF THE PROJECT

The project leader continues the project which was started 1995 by Prof. Dr. Frank Lempio.

Modelling of differential equations with discontinuous right-hand sides, dynamical systems with uncertainties, non-smooth optimization problems, and optimal control problems lead to differential equations with set-valued right-hand sides, so-called differential inclusions.

Within the research project "Set-Valued Numerical Analysis", differential inclusions are investigated qualitatively and quantitatively, and algorithms for their numerical solution are developed.

The numerical solution of such differential inclusions requires algorithms from set-valued numerical analysis, especially integration techniques for set-valued integrands and interpolation techniques for set-valued maps, based e.g. on set-valued finite element methods, set-valued divided differences and embeddings of convex compact sets. Especially, one focus is laid on the approximation of reachable sets at a given time which consist of all endpoints of admissible trajectories of a differential inclusion.

There are strong connections to the direcet discretization of optimal control problems, e.g. in questions on the (order of) convergence of the optimal control/trajectory of the discrete problems to the corresponding optimal control/trajectory of the continuous problem.

MINISYMPOSIA/SESSIONS

The project members organized the following minisymposia and sessions on set-valued numerics.

• invited Special Session "Approximation of Differential Inclusions and Control Problems 1-2"

  conference: 14th Viennese Conference on Optimal Control and Dynamic Games (OCDGND 2018) in Wien, Austria

  chair: Robert Baier, Elza Farkhi (Tel Aviv University, Israel)

• invited Special Session "Set-Valued Numerics and Control 1-2"

  conference: 13th Viennese Workshop on Optimal Control, and Dynamic Games (OCDGND 2015) in Wien, Austria

  chair: Robert Baier, Elza Farkhi (Tel Aviv University, Israel)

• invited Minisymposium "Set-dynamic Approaches with Applications in Car Engineering"

  conference: XXXIV Dynamics Days Europe (2014) in Bayreuth

  chair: Robert Baier, Thomas Lorenz (RheinMain Unversity in Wiesbaden)

• invited Special Session "Set-Valued Analysis for Optimal Control 1-2"

  conference: 12th Viennese Workshop on Optimal Control, Dynamic Games and Nonlinear Dynamics (OCDGND 2012) in Wien, Austria

  chair: Robert Baier

• invited Special Session MB-39 "Set-Valued Analysis for Control Problems"

  conference: 24th European Conference on Operational Research (EURO XXIV, 2010) in Lisbon, Portugal

  chair: Robert Baier

• Workshop "Set-valued Numerical Analysis and Robust Optimal Control"

  realization within the HIM Junior Trimester Program "Computational Mathematics" (2008) in Bonn, Germany

  organization: Robert Baier, Thomas Lorenz (formerly: University of Heidelberg)

LINKS

• The Hermann Minkowski Center of Geometry (Minerva Center at the Tel Aviv University)
  
• Minerva Foundation
  
• Hausdorff Research Institute for Mathematics (HIM) in Bonn, Germany