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Computation of Lyapunov Functions under State Constraints using Semidefinite Programming Hierarchies *

Marianne Souaiby 1 Aneel Tanwani 1 Didier Henrion 1
1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes
Abstract : We provide algorithms for computing a Lyapunov function for a class of systems where the state trajectories are constrained to evolve within a closed convex set. The dynamical systems that we consider comprise a differential equation which ensures continuous evolution within the domain, and a normal cone inclusion which ensures that the state trajectory remains within a prespecified set at all times. Finding a Lyapunov function for such a system boils down to finding a function which satisfies certain inequalities on the admissible set of state constraints. It is well-known that this problem, despite being convex, is computationally difficult. For conic constraints, we provide a discretization algorithm based on simplicial partitioning of a sim-plex, so that the search of desired function is addressed by constructing a hierarchy (associated with the diameter of the cells in the partition) of linear programs. Our second algorithm is tailored to semi-algebraic sets, where a hierarchy of semidefinite programs is constructed to compute Lyapunov functions as a sum-of-squares polynomial.
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Submitted on : Monday, September 14, 2020 - 12:55:36 PM
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  • HAL Id : hal-02937714, version 1
  • ARXIV : 2009.06885

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Marianne Souaiby, Aneel Tanwani, Didier Henrion. Computation of Lyapunov Functions under State Constraints using Semidefinite Programming Hierarchies *. 2020. ⟨hal-02937714v1⟩

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