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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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https://hal.inria.fr/inria-00636541
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Submitted on : Thursday, October 27, 2011 - 4:33:34 PM
Last modification on : Monday, October 11, 2021 - 2:22:06 PM

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

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