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Optimal control with hysteresis nonlinearity and multidimensional Play operator. (English) Zbl 1218.49004

Summary: 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.

MSC:

49J15 Existence theories for optimal control problems involving ordinary differential equations
49J52 Nonsmooth analysis
49L20 Dynamic programming in optimal control and differential games
47J40 Equations with nonlinear hysteresis operators
34C55 Hysteresis for ordinary differential equations
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