Computation of lyapunov functions under state constraints using semidefinite programming hierarchies

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F20%3A00355986" target="_blank" >RIV/68407700:21230/20:00355986 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.ifacol.2020.12.1746" target="_blank" >http://dx.doi.org/10.1016/j.ifacol.2020.12.1746</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.ifacol.2020.12.1746" target="_blank" >10.1016/j.ifacol.2020.12.1746</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Computation of lyapunov functions under state constraints using semidefinite programming hierarchies

Popis výsledku v původním jazyce

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 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.

Název v anglickém jazyce

Computation of lyapunov functions under state constraints using semidefinite programming hierarchies

Popis výsledku anglicky

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 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.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

20205 - Automation and control systems

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Proceedings of the IFAC World Congress 2020

ISBN

—

ISSN

2405-8963

e-ISSN

2405-8963

Počet stran výsledku

6

Strana od-do

6281-6286

Název nakladatele

IFAC

Místo vydání

Laxenburg

Místo konání akce

Berlín

Datum konání akce

11. 7. 2020

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

000652593000302