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Relaxed controls for nonlinear fractional impulsive evolution equations. (English) Zbl 1263.49038
Summary: In this paper, we study optimal relaxed controls and relaxation of nonlinear fractional impulsive evolution equations. Firstly, the existence of piecewise continuous mild solutions for the original fractional impulsive control system is established. Secondly, a fractional impulsive relaxed control system is constructed by using a regular countably additive measure and convexifying the original control system. Thirdly, optimal relaxed controls and relaxation theorems are obtained. Finally, an application to initial-boundary value problems of fractional impulsive parabolic control systems is considered.
MSC:
49N25Impulsive optimal control problems
49J45Optimal control problems involving semicontinuity and convergence; relaxation
34A08Fractional differential equations
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