Dynamic programming for some optimal control problems with hysteresis

被引：0
|
作者：
Fabio Bagagiolo
机构：
[1] Università degli Studi di Padova Dipartimento di Matematica,
[2] Pura ed Applicata,undefined
[3] Via Belzoni 7 35131 Padova,undefined
[4] Italy,undefined
[5] e-mail: fbaga@math.unipd.it,undefined
来源：
Nonlinear Differential Equations and Applications NoDEA | 2002年 / 9卷
关键词：
Key words and phrases: Optimal control, Dynamic programming method, Viscosity solutions, Hysteresis.;
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摘要：
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.
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页码：149 / 174
页数：25
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