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Set-Valued Return Function and Generalized Solutions for Multiobjective Optimal Control Problems (MOC)

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Preprint
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Submission Date
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arXiv ID: 1110.1352
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arXiv
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Abstract

In this paper, we consider a multiobjective optimal control problem where the preference relation in the objective space is de?ned in terms of a pointed convex cone containing the origin, which de?nes 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.

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