Computation of lyapunov functions under state constraints using semidefinite programming hierarchies
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Computation of lyapunov functions under state constraints using semidefinite programming hierarchies
Original language description
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.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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OECD FORD branch
20205 - Automation and control systems
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Proceedings of the IFAC World Congress 2020
ISBN
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ISSN
2405-8963
e-ISSN
2405-8963
Number of pages
6
Pages from-to
6281-6286
Publisher name
IFAC
Place of publication
Laxenburg
Event location
Berlín
Event date
Jul 11, 2020
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
000652593000302