This article is cited in 15 papers

Internal approximations of reachable sets of control systems with state constraints

M. I. Gusev<sup>ab

a</sup> Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
^b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg

Abstract: We consider the approximation problem for reachable sets of a nonlinear control system with state constraints, which are given as the solution set of a nonlinear inequality or a system of inequalities. An analog of the penalty function method is proposed, which consists in replacing the original system with state constraints by an auxiliary system without constraints by means of the restriction of the set of velocities of the original system. This restriction (the right-hand side of the auxiliary system) depends on a scalar penalty coefficient. It is proved that approximating sets converge in the Hausdorff metric to the reachable set of the original system as the penalty coefficient tends to infinity. An estimate of the convergence rate is obtained.

Keywords: control system, reachable set, state constraints, invariance, penalty function method.

UDC: 517.977.1

Received: 30.07.2013

 English version: Proceedings of the Steklov Institute of Mathematics (Supplement Issues), 2014, 287, suppl. 1, S77–S92

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