COMPUTING CONTROLLED INVARIANT SETS FROM DATA USING CONVEX OPTIMIZATION
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F20%3A00344661" target="_blank" >RIV/68407700:21230/20:00344661 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1137/19M1305835" target="_blank" >https://doi.org/10.1137/19M1305835</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/19M1305835" target="_blank" >10.1137/19M1305835</a>
Alternative languages
Result language
angličtina
Original language name
COMPUTING CONTROLLED INVARIANT SETS FROM DATA USING CONVEX OPTIMIZATION
Original language description
This work presents a data-driven method for approximation of the maximum positively invariant (MPI) set and the maximum controlled invariant (MCI) set for nonlinear dynamical systems. The method only requires knowledge of a finite collection of one-step transitions of the discrete-time dynamics, without the requirement of segments of trajectories or the control inputs that effected the transitions to be available. The approach uses a novel characterization of the MPI and MCI sets as the solution to an infinite-dimensional linear programming (LP) problem in the space of continuous functions, with the optimum being attained by a (Lipschitz) continuous function under mild assumptions. The infinite-dimensional LP is then approximated by restricting the decision variable to a finite-dimensional subspace and by imposing the nonnegativity constraint of this LP only on the available data samples. This leads to a single finite-dimensional LP that can be easily solved using off-the-shelf solvers. We analyze the convergence rate and sample complexity, proving probabilistic as well as hard guarantees on the volume error of the approximations. The approach is very general, requiring minimal underlying assumptions. In particular, the dynamics is not required to be polynomial or even continuous (forgoing some of the theoretical results). Detailed numerical examples up to state-space dimension 10 with code available online demonstrate the method.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
20205 - Automation and control systems
Result continuities
Project
<a href="/en/project/GJ20-11626Y" target="_blank" >GJ20-11626Y: Koopman operator framework for control of complex nonlinear dynamical systems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
SIAM Journal on Control and Optimization
ISSN
0363-0129
e-ISSN
1095-7138
Volume of the periodical
58
Issue of the periodical within the volume
5
Country of publishing house
US - UNITED STATES
Number of pages
29
Pages from-to
2871-2899
UT code for WoS article
000584700500007
EID of the result in the Scopus database
2-s2.0-85095684696