COMPUTING CONTROLLED INVARIANT SETS FROM DATA USING CONVEX OPTIMIZATION

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

COMPUTING CONTROLLED INVARIANT SETS FROM DATA USING CONVEX OPTIMIZATION

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

COMPUTING CONTROLLED INVARIANT SETS FROM DATA USING CONVEX OPTIMIZATION

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

20205 - Automation and control systems

Projekt

<a href="/cs/project/GJ20-11626Y" target="_blank" >GJ20-11626Y: Koncept Koopmanova operátoru pro řízení komplexních nelineárních dynamických systémů</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

SIAM Journal on Control and Optimization

ISSN

0363-0129

e-ISSN

1095-7138

Svazek periodika

58

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

29

Strana od-do

2871-2899

Kód UT WoS článku

000584700500007

EID výsledku v databázi Scopus

2-s2.0-85095684696