INFINITE-HORIZON MULTIOBJECTIVE OPTIMAL CONTROL PROBLEMS FOR BOUNDED PROCESSES

This paper studies multiobjective optimal control problems in the discrete time framework and in the infinite horizon case for bounded processes. The paper generalizes to the multiobjective case results obtained for single-objective optimal control problems in that framework. The dynamics are governed by difference equations. Necessary conditions of Pareto optimality are presented namely Pontryagin maximum principles in the strong form and in the weak form. Sufficient conditions are also provided. Other notions of Pareto optimality are defined when the infinite series do not necessarily converge and links with these unbounded cases are established.