Multicriteria Optimal Control and Vectorial Hamilton-Jacobi Equation
In this paper we investigate a multicriteria optimal control problem associated to a preference relation based on the lexicographic order. We extend different notions of non-smooth analysis and control and show that the vector Value function is the unique vector lower semicontinuous solution to a suitable system of Hamilton-Jacobi equations in the sense of contingent solution or equivalently in the sense of extended viscosity solution.
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