A Feasibility Problem Approach For Reachable Set Approximation

Reachability and controllability analysis for dynamic control systems are powerful tools for numerous applications like trajectory prediction, system verification, collision avoidance or control strategy validation. The computation of reachable sets (and controllability sets) is a central part of this analysis. In this work we advance an algorithm for approximating reachable sets which is originally based on optimally controlled problems with distance functions as objectives. It was initially described 2009 by Baier and Gerdts. The advanced approach works without minimizing objective functions and is based on pure feasibility problems. Many of these feasibility problems are solved in parallel to check the reachability of discrete grid points of a reachable set which is approximated via an equidistant grid discretization. We use the concept of interior point methods to develop an algorithm for solving many feasibility problems synchronously. Through a suitable problem definition we achieve a sparse linear algebra structure within the interior point method which is utilized to speed up the algorithm significantly. The whole algorithm design aims for an efficient execution on parallel CPU hardware and SIMD architecture as well. As an application example we use the new algorithm to compute the controllability set of a satellite docking maneuver (DEOS mission). With a 13-dimensional state vector and 6-dimensional control vector this system of ordinary differential equations is quite challenging in the context of reachable sets and serves as a nice benchmark.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Bayreuth

Year

2015

Author dc:creator

• Jahn, Thomas U.

Contributors dc:contributor

• Grüne, Lars

Repository record source_url

https://epub.uni-bayreuth.de/id/eprint/2087/

OAI identifier oai:identifier

oai:epub.uni-bayreuth.de:2087