文章基本信息

标题：Computation of Lyapunov Functions under State Constraints using Semidefinite Programming Hierarchies
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作者：Marianne Souaiby ; Aneel Tanwani ; Didier Henrion 等
期刊名称：IFAC PapersOnLine
印刷版ISSN：2405-8963
出版年度：2020
卷号：53
期号：2
页码：6281-6286
DOI：10.1016/j.ifacol.2020.12.1746
语种：English
出版社：Elsevier
摘要：AbstractWe 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 simplex, 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.
关键词：KeywordsConstrained systemscopositive Lyapunov functionscomplementarity systemsconvex optimization