Controller design and value function approximation for nonlinear dynamical systems

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F16%3A00303440" target="_blank" >RIV/68407700:21230/16:00303440 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1016/j.automatica.2016.01.022" target="_blank" >http://dx.doi.org/10.1016/j.automatica.2016.01.022</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.automatica.2016.01.022" target="_blank" >10.1016/j.automatica.2016.01.022</a>

Result language

angličtina

Original language name

Controller design and value function approximation for nonlinear dynamical systems

Original language description

This work considers the infinite-time discounted optimal control problem for continuous time input-affine polynomial dynamical systems subject to polynomial state and box input constraints. We propose a sequence of sum-of-squares (SOS) approximations of this problem obtained by first lifting the original problem into the space of measures with continuous densities and then restricting these densities to polynomials. These approximations are tightenings, rather than relaxations, of the original problem and provide a sequence of rational controllers with value functions associated to these controllers converging (under some technical assumptions) to the value function of the original problem. In addition, we describe a method to obtain polynomial approximations from above and from below to the value function of the extracted rational controllers, and a method to obtain approximations from below to the optimal value function of the original problem, thereby obtaining a sequence of asymptotically optimal rational controllers with explicit estimates of suboptimality. Numerical examples demonstrate the approach.

Czech name

—

Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BC - Theory and management systems

OECD FORD branch

—

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2016

Confidentiality

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

Name of the periodical

Automatica

ISSN

0005-1098

e-ISSN

—

Volume of the periodical

67

Issue of the periodical within the volume

May

Country of publishing house

GB - UNITED KINGDOM

Number of pages

13

Pages from-to

54-66

UT code for WoS article

000373540300006

EID of the result in the Scopus database

2-s2.0-84960432002