TY - GEN
T1 - A topological method for finding invariant sets of switched systems
AU - Fribourg, Laurent
AU - Goubault, Eric
AU - Putot, Sylvie
AU - Mohamed, Sameh
N1 - Publisher Copyright:
© 2016 ACM.
PY - 2016/4/11
Y1 - 2016/4/11
N2 - We revisit the problem of finding controlled invariants sets (viability), for a class of differential inclusions, using topological methods based on Wafizewski property. In many ways, this generalizes the Viability Theorem approach, which is itself a generalization of the Lyapunov function approach for systems described by ordinary differential equations. We give a computable criterion based on SoS methods for a class of differential inclusions to have a non-empty viability kernel within some given region. We use this method to prove the existence of (controlled) invariant sets of switched systems inside a region described by a polynomial template, both with time-dependent switching and with state-based switching through a finite set of hypersurfaces. A Matlab implementation allows us to demonstrate its use.
AB - We revisit the problem of finding controlled invariants sets (viability), for a class of differential inclusions, using topological methods based on Wafizewski property. In many ways, this generalizes the Viability Theorem approach, which is itself a generalization of the Lyapunov function approach for systems described by ordinary differential equations. We give a computable criterion based on SoS methods for a class of differential inclusions to have a non-empty viability kernel within some given region. We use this method to prove the existence of (controlled) invariant sets of switched systems inside a region described by a polynomial template, both with time-dependent switching and with state-based switching through a finite set of hypersurfaces. A Matlab implementation allows us to demonstrate its use.
KW - Control
KW - Cyber-Physical Systems
KW - Differential Inclusion
KW - Viability
U2 - 10.1145/2883817.2883822
DO - 10.1145/2883817.2883822
M3 - Conference contribution
AN - SCOPUS:84966663973
T3 - HSCC 2016 - Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control
SP - 61
EP - 70
BT - HSCC 2016 - Proceedings of the 19th International Conference on Hybrid Systems
PB - Association for Computing Machinery, Inc
T2 - 19th International Conference on Hybrid Systems: Computation and Control, HSCC 2016
Y2 - 12 April 2016 through 14 April 2016
ER -