Evolutionary Multicriteria Optimization for Improved Design of Optimal Control Systems

Abstract

Design of optimal control systems has been traditionally based on minimization of a quadratic performance measure, which typically is an integral of a weighted linear combination of x(T) Qx and u(T) Ru. Choice of the linear weighting matrices Q and R based on heuristics and experiments are required to ascertain a satisfactory optimal value. In this paper we present a mathematical reformulation of the optimal control problem and restructure it with multiple performance indices instead of a single performance index. We thus reformulate the control system design as a multicriteria optimization problem. By reference to a Pareto set we assign a fitness values. We also show that this reformulation allows us to construct a nonlinear function of the state which we use as a feedback for the control. By use of this non-linear state feedback we demonstrate that the time response of the system, as it stabilizes, is considerably improved. Computer simulations and comparisons of linear and nonlinear state feedback convincingly demonstrates the effectiveness of such an approach.