TY - GEN
T1 - Simulation-aided reachability and local gain analysis for nonlinear dynamical systems
AU - Tan, Weehong
AU - Topcu, Ufuk
AU - Seiler, Peter
AU - Balas, Gary
AU - Packard, Andrew
PY - 2008/12/1
Y1 - 2008/12/1
N2 - We analyze reachability properties and local input/output gains of systems with polynomial vector fields. Upper bounds for the reachable set and nonlinear system gains are characterized by polynomial Lyapunov (storage) functions satisfying certain bilinear constraints. A methodology utilizing information from simulations to generate Lyapunov function candidates satisfying necessary conditions for bilinear constraints is proposed. The suitability of Lyapunov function candidates are assessed solving linear sum-of-squares optimization problems. Qualified candidates are used to compute upper bounds for the reachable set and nonlinear system gains and to initialize further coordinate-wise affine optimization. We illustrate the method on several examples from the literature.
AB - We analyze reachability properties and local input/output gains of systems with polynomial vector fields. Upper bounds for the reachable set and nonlinear system gains are characterized by polynomial Lyapunov (storage) functions satisfying certain bilinear constraints. A methodology utilizing information from simulations to generate Lyapunov function candidates satisfying necessary conditions for bilinear constraints is proposed. The suitability of Lyapunov function candidates are assessed solving linear sum-of-squares optimization problems. Qualified candidates are used to compute upper bounds for the reachable set and nonlinear system gains and to initialize further coordinate-wise affine optimization. We illustrate the method on several examples from the literature.
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U2 - 10.1109/CDC.2008.4739425
DO - 10.1109/CDC.2008.4739425
M3 - Conference contribution
AN - SCOPUS:62949232002
SN - 9781424431243
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 4097
EP - 4102
BT - Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008
T2 - 47th IEEE Conference on Decision and Control, CDC 2008
Y2 - 9 December 2008 through 11 December 2008
ER -