Research on multiobjective optimization control for nonlinear unknown systems

This paper is focused on the optimal control problem of the nonlinear unknown systems with multiobjectives. The concept of system output response function based upon system input sequence over time is proposed, and the problem is formulated accordingly. Considering the fact that a finite response curve set is easy to be obtained, we employ the Pareto rule-base and the approximate Pareto control algorithm for multiobjective control optimization based on the finite response curve set. In this way, an easy method to find a Pareto rule-base for the complicated multiobjective optimal control problem that converts the problem to the one that can be resolved only in a finite set consisting of input-output date and curves over time is presented. It can guarantee that every rule´s input and output base point is optimally matched in Pareto sense within the known set of input and output of the system. Moreover, some sufficient conditions are obtained for the conventional fuzzy control algorithm to be a Pareto one. It is shown that if the rule-base is composed of Pareto rules, then for any inputs between two rule base-point, the corresponding output of the algorithm is also bounded by the two corresponding out base-points of the two rules. From the view of approximation, the Pareto algorithm can guarantee the system response is of Pareto performance relative to the objectives. As an illustration, the theory is applied to Monotone Inertial System. Simulation results agree with theories presented in this paper, and show that the fuzzy controller based on the Pareto rule-base presents very good behaviors in adaptivity, robustness and tracking with time-varying setpoint.