1. Reachability and Control Synthesis for Piecewise-Affine Hybrid Systems on Simplices.
- Author
-
Habets, L. C. G. J. M., Collins, P. J., and van Schuppen, J. H.
- Subjects
- *
LINEAR algebra , *DYNAMIC programming , *COMPUTATIONAL mathematics , *PROGRAMMING languages , *AFFINE geometry , *NUMERICAL integration , *ROBOTICS research , *ELECTRONICS - Abstract
In this paper, we consider the synthesis of control laws for piecewise-affine hybrid systems on simplices. The construction is based on the solution to the control-to-facet problem at the continuous level, and on dynamic programming at the discrete level. The construction is given as an explicit algorithm using only linear algebra and reach-set computations for automata; no numerical integration is required. The method is conservative, in that it may fail to find a control law where one exists, but one cannot hope for a sharp algorithm for control synthesis since reachability for piece- wise-affine hybrid systems is undecidable. [ABSTRACT FROM AUTHOR]
- Published
- 2006
- Full Text
- View/download PDF