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Optimal control problems governed by time dependent subdifferential operators with delay. (English) Zbl 1345.49005

Summary: This article is devoted to the study, in the infinite dimensional setting, of a Bolza-type problem governed by a class of functional evolution inclusion, which involves a time-dependent subdifferential operator with a time-delay perturbation. We present a relaxation result associated with such equations, where the controls are Young measures, in order to show the existence of an optimal solution under a suitable convexity assumption.

MSC:

49J21 Existence theories for optimal control problems involving relations other than differential equations
49J52 Nonsmooth analysis
49J53 Set-valued and variational analysis
49J45 Methods involving semicontinuity and convergence; relaxation
34G25 Evolution inclusions
34A60 Ordinary differential inclusions
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References:

[1] DOI: 10.1016/0022-247X(83)90143-9 · Zbl 0517.49002
[2] Castaing C., J. Nonlinear Convex Anal 5 pp 131– (2004)
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[7] DOI: 10.1090/surv/015
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