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The problem of optimal control with reflection studied through a linear optimization problem stated on occupational measures. (English) Zbl 1180.49025

Summary: We obtain a linear programming characterization for the minimum cost associated with finite dimensional reflected optimal control problems. In order to describe the value functions, we employ an infinite dimensional dual formulation instead of using the characterization via Hamilton-Jacobi partial differential equations. In this paper we consider control problems with both infinite and finite horizons. The reflection is given by the normal cone to a proximal retract set.

MSC:

49K21 Optimality conditions for problems involving relations other than differential equations
34K35 Control problems for functional-differential equations
49L20 Dynamic programming in optimal control and differential games
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
93B18 Linearizations
93C15 Control/observation systems governed by ordinary differential equations
49N15 Duality theory (optimization)
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