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Bilevel optimal control with final-state-dependent finite-dimensional lower level. (English) Zbl 1333.49008

Summary: In this paper we discuss special bilevel optimal control problems where the upper level problem is an optimal control problem of ODEs with control and terminal constraints and the lower level problem is a finite-dimensional parametric optimization problem where the parameter is the final state of the state variable of the upper level. We tackle this problem using tools from nonsmooth analysis, optimization in Banach spaces, and bilevel programming to derive necessary optimality conditions of linearized Pontryagin-type.

MSC:

49J21 Existence theories for optimal control problems involving relations other than differential equations
49K21 Optimality conditions for problems involving relations other than differential equations
90C30 Nonlinear programming
90C48 Programming in abstract spaces
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