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Set-valued return function and generalized solutions for multiobjective optimal control problems (MOC). (English) Zbl 1273.49022

Summary: In this paper, we consider a multiobjective optimal control problem where the preference relation in the objective space is defined in terms of a pointed convex cone containing the origin, which defines generalized Pareto optimality. For this problem, we introduce the set-valued return function \(V\) and provide a unique characterization for \(V\) in terms of contingent derivative and coderivative for set-valued maps, which extends two previously introduced notions of generalized solution to the Hamilton-Jacobi equation for single objective optimal control problems.

MSC:

49J53 Set-valued and variational analysis
49K15 Optimality conditions for problems involving ordinary differential equations
49L20 Dynamic programming in optimal control and differential games
54C60 Set-valued maps in general topology
90C29 Multi-objective and goal programming
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