Preprint 38/2000

Dynamic programming for some optimal control problems with hysteresis

Fabio Bagagiolo

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Submission date: 26. May. 2000
Pages: 27
published in: Nonlinear differential equations and applications, 9 (2002) 2, p. 149-174 
DOI number (of the published article): 10.1007/s00030-002-8122-0
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We study an infinite horizon optimal control problem for a system with two state variables. One of them has the evolution governed by a controlled ordinary differential equation and the other one is related to the latter by a hysteresis relation, represented here by either a play operator or a Prandtl-Ishlinskii operator. By dynamic programming, we derive the corresponding (discontinuous) first order Hamilton-Jacobi equation, which in the first case is of finite dimension and in the second case is of infinite dimension. In both cases we prove that the value function is the only bounded uniformly continuous viscosity solution of the equation.

24.11.2021, 02:11