Infinite horizon multiobjective optimal control problems in the discrete time case

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 optimization
• Pareto optimality
• discrete time optimal control
• infinite horizon

AMS Subject Classifications::

• 90C29
• 90C46
• 93C55
• 49K99

Acknowledgement

The author thanks Joel Blot for all his useful comments.