In the proceedings of the Conference on Decision and Control, pp. 4097-4102, 2008 (W. Tan, P. Seiler, G. Balas, and A. Packard).
@INPROCEEDINGS{4739425,
title={Simulation-aided reachability and local gain analysis for nonlinear dynamical systems},
author={Weehong Tan and Topcu, U. and Seiler, P. and Balas, G. and Packard, A.},
booktitle={Decision and Control, 2008. CDC 2008. 47th IEEE Conference on},
year={2008},
month={Dec.},
volume={},
number={},
pages={4097-4102},
abstract={We analyze reachability properties and local inputoutput 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.},
keywords={Lyapunov methods, bilinear systems, nonlinear dynamical systems, polynomials, reachability analysisbilinear constraints, linear sum-of-squares optimization problems, local gain analysis, local input-output gains, nonlinear dynamical systems, polynomial Lyapunov functions, polynomial vector fields, reachability properties, simulation-aided reachability},
doi={10.1109CDC.2008.4739425},
ISSN={0191-2216},
}