Relaxation in nonconvex optimal control problems described by fractional differential equations |
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Authors: | Xiaoyou Liu Zhenhai Liu Xi Fu |
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Institution: | 1. School of Mathematics and Physics, University of South China, Hengyang 421001, Hunan Province, PR China;2. College of Sciences, Guangxi University for Nationalities, Nanning 530006, Guangxi Province, PR China;3. Department of Mathematics, Shaoxing University, Shaoxing 312000, Zhejiang Province, PR China |
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Abstract: | We consider the minimization problem of an integral functional with integrand that is not convex in the control on solutions of a control system described by fractional differential equation with mixed nonconvex constraints on the control. A relaxation problem is treated along with the original problem. It is proved that, under general assumptions, the relaxation problem has an optimal solution, and that for each optimal solution there is a minimizing sequence of the original problem that converges to the optimal solution with respect to the trajectory, the control, and the functional in appropriate topologies simultaneously. |
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Keywords: | Fractional differential equation Optimal control Relaxation property Nonconvex constraint Feedback control |
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