Infinite-dimensional multiobjective optimal control in continuous time

TL;DR

This paper extends multiobjective optimal control theory to infinite-dimensional spaces with less restrictive smoothness, providing necessary and sufficient conditions for Pareto optimality in such complex systems.

Contribution

It generalizes existing single-objective control results to multiobjective cases in infinite-dimensional spaces with weaker smoothness assumptions.

Findings

Established Pontryagin maximum principles for Pareto optimality.

Provided both necessary and sufficient conditions for optimality.

Extended control theory to infinite-dimensional, multiobjective, continuous-time systems.

Abstract

This paper studies multiobjective optimal control problems in the continuous-time framework when the space of states and the space of controls are infinite-dimensional and with lighter smoothness assumptions than the usual ones. The paper generalizes to the multiobjective case existing results for single-objective optimal control problems in that framework. The dynamics are governed by differential equations and a finite number of terminal equality and inequality constraints are present. Necessary conditions of Pareto optimality are provided namely Pontryagin maximum principles in the strong form. Sufficient conditions are also provided.