Hamiltonian Formalism for the Problem of Optimal Motion Control under Multiple Criteria

Abstract

This paper describes methods for optimizing solutions to problems of controlled dynamics under multiple criteria. Such problems are usually solved by reduction to scalarized costs. However, preferable in realistic cases is the analysis of the whole Pareto front with description of its evolutionary dynamics. This is done via the introduction of vector-valued multiobjective dynamic programming similar to the classical approach described in [1]. It is shown that, under certain conditions, a multiobjective analogue of the classical principle of optimality holds for the introduced vector-valued cost function. As a result, a vector-valued version of the Hamilton–Jacobi–Bellman equation is introduced and the dynamics of the whole Pareto front is presented.