Weighting Matrix Selection Method for LQR Design Based on a Multi-Objective Evolutionary Algorithm

Abstract

This paper introduces an application of Multi-Objective Evolution Algorithm (MOEA) to design Q and R weighting matrices in Linear Quadratic regulators (LQR). Considering the difficulty of designing weighting matrices for a linear quadratic regulator, a multi-objective evolutionary algorithm based approach is proposed. The LQR weighting matrices, state feedback control rate and consequently the optimal controller are obtained by means of establishing the multi-objective optimization model of LQR weighting matrices and applying MOEA to it, which makes control system meet multiple performance indexes simultaneously. Controller of double inverted pendulum system is designed using the proposed approach. Simulation results show that it has shorter adjusting time and smaller amplitude value deviating from steady-state than a Non-dominated Sorting Genetic Algorithm LQR ( NSGA- LQR )weighting matrices design approach.

A Tuning Algorithm for LQ-PID Controllers using the Combined Time - and Frequency-Domain Control Method

“…In linear optimal control, the linear quadratic regulator (LQR) problem is to find the optimal feedback control law to minimize the quadratic performance criterion with respect to the states and inputs via weighting matrices Q and R [3][4][5]. Thus the central issue remains of how to relate the weighting matrices in the quadratic performance criterion to classical specifications in the time and frequency domains for the control system design [6][7][8][9].…”