Simulation-aided reachability and local gain analysis for nonlinear dynamical systems

Weehong Tan; Ufuk Topcu; Peter Seiler; Gary Balas; Andrew Packard

doi:10.1109/CDC.2008.4739425

Simulation-aided reachability and local gain analysis for nonlinear dynamical systems

Weehong Tan, Ufuk Topcu, Peter Seiler, Gary Balas, Andrew Packard

Aerospace Engineering and Mechanics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

15 Scopus citations

Abstract

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.

Original language	English (US)
Title of host publication	Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008
Pages	4097-4102
Number of pages	6
DOIs	https://doi.org/10.1109/CDC.2008.4739425
State	Published - Dec 1 2008
Event	47th IEEE Conference on Decision and Control, CDC 2008 - Cancun, Mexico Duration: Dec 9 2008 → Dec 11 2008

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0191-2216

Other

Other	47th IEEE Conference on Decision and Control, CDC 2008
Country	Mexico
City	Cancun
Period	12/9/08 → 12/11/08

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10.1109/CDC.2008.4739425

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Simulation-aided reachability and local gain analysis for nonlinear dynamical systems. / Tan, Weehong; Topcu, Ufuk; Seiler, Peter; Balas, Gary; Packard, Andrew.

Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008. 2008. p. 4097-4102 4739425 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Tan, W, Topcu, U, Seiler, P, Balas, G & Packard, A 2008, Simulation-aided reachability and local gain analysis for nonlinear dynamical systems. in Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008., 4739425, Proceedings of the IEEE Conference on Decision and Control, pp. 4097-4102, 47th IEEE Conference on Decision and Control, CDC 2008, Cancun, Mexico, 12/9/08. https://doi.org/10.1109/CDC.2008.4739425

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title = "Simulation-aided reachability and local gain analysis for nonlinear dynamical systems",

abstract = "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.",

author = "Weehong Tan and Ufuk Topcu and Peter Seiler and Gary Balas and Andrew Packard",

year = "2008",

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doi = "10.1109/CDC.2008.4739425",

language = "English (US)",

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series = "Proceedings of the IEEE Conference on Decision and Control",

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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

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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 -

Simulation-aided reachability and local gain analysis for nonlinear dynamical systems

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