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Journal Articles SIAM Journal on Control and Optimization Year : 2011

Optimal Control with Hysteresis Nonlinearity and Multidimensional Play Operator

Abstract

We investigate an optimal control of a system with a specific form of hysteresis. The hysteresis operator considered in the article is a Play operator which generalizes the usual Play operator defined through a one dimensional domain set. The main novelty of this paper lies in the study of the Play operator with a set of feasible states which is multidimensional and possibly nonconvex. The key ingredient of our approach is the interpretation of the hysteresis control systems through a reflected control system. We provide a characterization of the value in terms of the unique solution to a Hamilton-Jacobi-Bellman variational inequality.
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Dates and versions

inria-00636541 , version 1 (27-10-2011)

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Anastasia Goudovich, Marc Quincampoix. Optimal Control with Hysteresis Nonlinearity and Multidimensional Play Operator. SIAM Journal on Control and Optimization, 2011, 49, pp.788-807. ⟨10.1137/090770011⟩. ⟨inria-00636541⟩
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