On reachability analysis for nonlinear control systems with state constraints

Mikhail  Gusev

doi:10.3934/proc.2015.0579

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2015, Volume 2015: 579-587. Doi: 10.3934/proc.2015.0579 open access

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On reachability analysis for nonlinear control systems with state constraints

Mikhail Gusev^1,

1.
N.N.Krasovskii Institute of Mathematics and Mechanics, S.Kovalevskaya str., 16, 620099, Ekaterinburg

Received: August 31, 2014

Revised: January 31, 2015

Published: October 2015

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Abstract

The paper is devoted to the problem of approximating reachable sets of a nonlinear control system with state constraints given as a solution set for a nonlinear inequality. A procedure to remove state constraints is proposed; this procedure consists in replacing a primary system by an auxiliary system without state constraints. The equations of the auxiliary system depend on a small parameter. It is shown that a reachable set of the primary system may be approximated in the Hausdorff metric by reachable sets of the auxiliary system when the small parameter tends to zero. The estimates of the rate of convergence are given.

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Mathematics Subject Classification: Primary: 93B03, 93C15; Secondary: 49J15.

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