Reachability and control synthesis for piecewise-affine hybrid systems on simplices

• Published in: IEEE transactions on automatic control Vol. 51; no. 6; pp. 938 - 948
• Main Authors: Habets, L.C.G.J.M., Collins, P.J., van Schuppen, J.H.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.06.2006; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Automata; Automatic control; Construction; Control system synthesis; Control systems; Discrete-event system (DES); exit facet; Hybrid systems; Law; Linear algebra; Mathematical models; Physics computing; piecewise-affine hybrid systems; Power engineering and energy; Power engineering computing; reachability; Robust stability; Safety; simplex; stability; Synthesis; Systems engineering and theory
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2006.876952

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 piecewise-affine hybrid systems is undecidable.