Geodesic
On the penalty function method in the problem of constructing reachable sets for control systems with state constraints
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 1, pp. 81-86

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The paper is devoted to the problem of constructing reachable sets for a nonlinear control system with state constraints given in the form of inequalities. An analog of the penalty function method is proposed; it consists in replacing the original system with state constraints by an auxiliary system without state constraints. The right-hand side of the auxiliary system is a modification of the right-hand side of the original system and depends on a scalar parameter (a penalty coefficient). Under certain conditions, we show that a reachable set of the original system can be approximated from within in the Hausdorff metric by reachable sets of auxiliary systems as the penalty coefficient tends to infinity.
Keywords: control system, reachable set, state constraints, penalty function method. 
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     author = {M. I. Gusev},
     title = {On the penalty function method in the problem of constructing reachable sets for control systems with state constraints},
     journal = {Trudy Instituta matematiki i mehaniki},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2013_19_1_a7/}
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M. I. Gusev. On the penalty function method in the problem of constructing reachable sets for control systems with state constraints. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 1, pp. 81-86. http://geodesic.mathdoc.fr/item/TIMM_2013_19_1_a7/