Infinite horizon multiobjective optimal control problems in the discrete time case

Abstract

Abstract This article studies multiobjective optimal control problems in the discrete time framework and in the infinite horizon case. The functions appearing in the problems satisfy smoothness conditions. This article generalizes to the multiobjective case results obtained for single-objective optimal control problems in that framework. The dynamics are governed by difference equations or difference inequations. Necessary conditions of Pareto optimality are presented, namely Pontryagin maximum principles in the weak form and in the strong form. Sufficient conditions are also provided. Other notions of Pareto optimality are defined when the infinite series do not necessarily converge. Keywords: multiobjective optimizationPareto optimalitydiscrete time optimal controlinfinite horizonAMS Subject Classifications:: 90C2990C4693C5549K99 Acknowledgement The author thanks Joel Blot for all his useful comments.