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November  2001, 1(4): 443-462. doi: 10.3934/dcdsb.2001.1.443

An infinite horizon optimal control problem for some switching systems

Fabio Bagagiolo 1,

1. 

Dipartimento di Matematica, Universitá di Trento, Via Sommarive, 14, 38050 Povo di Trento (TN), Italy

Received  December 2000 Revised  July 2001 Published  September 2001

We study an infinite horizon optimal control problem for a system with two state variables. They are respectively the input and the output of either a delayed relay or a finite sum of delayed relays. The system exhibits hysteresis and the output of the relay is discontinuous. We consider two different switching rules for the relay. We characterize the value functions by the unique viscosity solution of some suitably coupled Dirichlet problems for Hamilton-Jacobi equations.
Keywords: exit time problems, viscosity solutions, Optimal control, hysteresis..
Mathematics Subject Classification: 47J40, 49J15, 49L2.
Citation: Fabio Bagagiolo. An infinite horizon optimal control problem for some switching systems. Discrete & Continuous Dynamical Systems - B, 2001, 1 (4) : 443-462. doi: 10.3934/dcdsb.2001.1.443
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