Set-Valued Return Function and Generalized Solutions for Multiobjective Optimal Control Problems (MOC)
Alexis Guigue · SIAM Journal on Control and Optimization · 2013
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.