A Computational Method for Non-Convex Reachable Sets using Optimal Control

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

Smart-Link: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7074386
ISBN/ISSN/ISMV Nummer: 978-3-9524173-9-3
Keywords: optimal control problems; direct discretization methods for optimal control; distance function
Mathematics Subject Classification Code: 93B03 (49J21 49J15 34A60 49J53)
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Abstract:

A computational method for the approximation of reachable sets for non-linear dynamic systems is suggested. The method is based on a discretization of the interesting region and a projection onto grid points. The projections require to solve optimal control problems which are solved by a direct discretization approach. These optimal control problems allow a flexible formulation and it is possible to add non-linear state and/or control constraints and boundary conditions to the dynamic system. Numerical results for non-convex reachable sets are presented. Possible applications include robust optimal control problems.

Contents:

I. Introduction
II. The Algorithm
III. Numerical Examples
IV. Extensions and Related Problems
V. Conclusions and Future Works

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