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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 : Thursday, October 8, 2020 - 3:45:14 PM
Last modification on : Wednesday, November 3, 2021 - 7:26:45 AM


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Marianne Souaiby, Aneel Tanwani, Didier Henrion. Computation of Lyapunov Functions under State Constraints using Semidefinite Programming Hierarchies. 21st IFAC World Congress, Jul 2020, Berlin virtual), Germany. ⟨10.1016/j.ifacol.2020.12.1746⟩. ⟨hal-02937714v2⟩



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