Multi-Objective Optimization Control for Discrete-Time Nonlinear Systems: A Policy Iteration Approach

摘要

This paper is concerned with the Multi-Objective Optimization Control (MOOC) problem for a discrete-time nonlinear system. We would like to seek one Pareto optimal control policy, under which no further changes can make one performance index better without at the same time making at least one performance index worse. To do this, we develop a new Multi-Objective Policy Iteration (MOPI) algorithm. Two termination criteria are proposed to effectively prevent the policy bouncing in the Pareto optimal set. Furthermore, we provide rigorous analysis to show that the developed MOPI algorithm converges to one Pareto optimal control policy under the proposed termination criteria. Besides that, the MOOC problem for discrete-time linear system with quadratic performance index is studied, which is a special case of the former problem for discrete-time nonlinear system. Finally, we give a simulation example to show the effectiveness of the proposed MOPI algorithm.