Title data
Baier, Robert ; Gerdts, Matthias ; Xausa, Ilaria:
Approximation of reachable sets using optimal control algorithms.
Department of Mathematics, University of Bayreuth
Bayreuth
,
2012
.  44 p.
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Abstract in another language
We investigate and analyze a computational method for the approximation of reachable sets for nonlinear dynamic systems. The method uses grids to cover the region of interest and the distance function to the reachable set evaluated at grid points. A convergence analysis is provided and shows the convergence of three different types of discrete set approximations to the reachable set. The distance functions can be computed numerically by suitable optimal control problems in combination with direct discretization techniques which allows
adaptive calculations of reachable sets. Several numerical examples with nonconvex reachable sets are presented.
Further data
Item Type:  Preprint, postprint, working paper, discussion paper 

Refereed:  Yes 
Additional notes:  original version from April 2010, published as technical report in October 2011, updated in October 2012 Contents: 1. Introduction 2. Proximal Normals and Inner/Outer Approximation of Sets 2.1 Set Representation Techniques 2.3 Inner/Outer Approximation of Sets 3. Convergence Analysis 3.1 Properties and Approximations of Reachable Sets 3.2 Discrete Approximation of Reachable Sets 4. Numerical Realization 4.1 DFOG Method 5. Numerical Examples 5.1 Kenderov's Example 5.2 Bilinear Example 5.3 Adaptive Version 5.4 Example from a PursuitEvasion Game 6. Outline 
Keywords:  reachable sets; optimal control; direct discretization 
Subject classification:  Mathematics Subject Classification Code: 49J15 49M25 93B03 93C10 (90C30) 
Institutions of the University:  Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) Profile Fields Profile Fields > Advanced Fields Profile Fields > Advanced Fields > Nonlinear Dynamics 
Result of work at the UBT:  Yes 
DDC Subjects:  500 Science > 510 Mathematics 
Date Deposited:  11 Apr 2015 21:00 
Last Modified:  13 Apr 2015 08:41 
URI:  https://eref.unibayreuth.de/id/eprint/10174 
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 Approximation of reachable sets using optimal control algorithms. (deposited 11 Apr 2015 21:00) [Currently Displayed]