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

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

2011-10-06

arxiv.org/abs/1110.1352v1

Mathematics

Optimization and Control

29 pages, submitted to SICON

Scientific paper

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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