Abstract.
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.
Similar content being viewed by others
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bagagiolo, F. Dynamic programming for some optimal control problems with hysteresis. NoDEA, Nonlinear differ. equ. appl. 9, 149–174 (2002). https://doi.org/10.1007/s00030-002-8122-0
Issue Date:
DOI: https://doi.org/10.1007/s00030-002-8122-0