Distributionally Robust Lyapunov Function Search Under Uncertainty

This paper develops methods for proving Lyapunov stability of dynamical systems subject to disturbances with an unknown distribution. We assume only a finite set of disturbance samples is available and that the true online disturbance realization may be drawn from a different distribution than the g...

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Bibliographic Details
Main Authors Long, Kehan, Yi, Yinzhuang, Cortes, Jorge, Atanasov, Nikolay
Format Journal Article
LanguageEnglish
Published 03.12.2022
Subjects
Computer Science - Robotics
Mathematics - Optimization and Control
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DOI10.48550/arxiv.2212.01554

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Summary:This paper develops methods for proving Lyapunov stability of dynamical systems subject to disturbances with an unknown distribution. We assume only a finite set of disturbance samples is available and that the true online disturbance realization may be drawn from a different distribution than the given samples. We formulate an optimization problem to search for a sum-of-squares (SOS) Lyapunov function and introduce a distributionally robust version of the Lyapunov function derivative constraint. We show that this constraint may be reformulated as several SOS constraints, ensuring that the search for a Lyapunov function remains in the class of SOS polynomial optimization problems. For general systems, we provide a distributionally robust chance-constrained formulation for neural network Lyapunov function search. Simulations demonstrate the validity and efficiency of either formulation on non-linear uncertain dynamical systems.
DOI:10.48550/arxiv.2212.01554