Abstract

Selecting appropriate weighting matrices for desired linear quadratic regulator (LQR) controller design using evolutionary algorithms is presented in this paper. Obviously, it is not easy to determine the appropriate weighting matrices for an optimal control system and a suitable systematic method is not presented for this goal. In other words, there is no direct relationship between weighting matrices and control system characteristics, and selecting these matrices is done by using trial and error based on designer’s experience. In this paper, we use the particle swarm optimization (PSO) method which is inspired by the social behavior of fish and birds in finding food sources to determine these matrices. Stable convergence characteristics and high calculation speed are the advantages of the proposed method. Simulation results demonstrate that in comparison with genetic algorithms (GAs), the PSO method is very efficient and robust in designing of optimal LQR controller.

Key words: Linear quadratic regulator (LQR), weighting matrices, particle swarm optimization, genetic algorithm.