State constrained patchy feedback stabilization

Fabio S. Priuli

doi:10.3934/mcrf.2015.5.141

Article Contents

2015, Volume 5, Issue 1: 141-163. Doi: 10.3934/mcrf.2015.5.141

This issue Previous Article A linear-quadratic optimal control problem for mean-field stochastic differential equations in infinite horizon Next Article A quantitative internal unique continuation for stochastic parabolic equations

State constrained patchy feedback stabilization

Fabio S. Priuli^1,

1.
Istituto per le Applicazioni del Calcolo “M. Picone", Consiglio Nazionale delle Ricerche, Via dei Taurini 19, I-00185 Roma

Received: October 31, 2013

Revised: March 31, 2014

Published: February 2015

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Abstract

We construct a patchy feedback for a general control system on $\mathbb{R}^d$ which realizes practical stabilization to a target set $\Sigma$, when the dynamics is constrained to a given set of states $S$. The main result is that $S$--constrained asymptotically controllability to $\Sigma$ implies the existence of a discontinuous practically stabilizing feedback. Such a feedback can be constructed in ``patchy'' form, a particular class of piecewise constant controls which ensure the existence of local Carathéodory solutions to any Cauchy problem of the control system and which enjoy good robustness properties with respect to both measurement errors and external disturbances.

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Mathematics Subject Classification: 34A34, 34A36, 34H05, 34H15, 93D15, 93D09.

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