The selection of suitable weighting matrices for the desired linear quadratic regulator (LQR) controller design using evolutionary algorithms is presented in This item. Obviously, it is not easy to determine the appropriate weighting matrices for an optimal control system and no suitable systematic method is presented to achieve this goal. In other words, there is no direct relationship between the weighting matrices and the characteristics of the control system and the selection of these matrices is done by trial and error based on the experience of the designer. In this article, we use the Particle Swarm Optimization (PSO) method which is inspired by the social behavior of fish and birds in searching for food sources to determine these matrices. Stable convergence characteristics and high calculation speed are advantages of the proposed method. The simulation results demonstrate that compared with genetic algorithms (GA), the PSO method is very efficient and robust in designing an optimal LQR controller.IntroductionIn designing many systems and solving problems, we need to choose one response from some possible responses as the optimal response response. But due to the wide range of responses, not all of them can be tested and then this testing must be done stochastically. On the other hand, this stochastic procedure should lead to the best answer [1]. Due to its simple implementation in engineering problems, it has received significant attention in linear quadratic optimal control theory. Linear quadratic optimal control is important to modern control theory and can be easily implemented for engineering applications and is the basic theory for other control techniques. However, in a special case where the cost function is a linear quadratic function, the o...... middle of paper ......o. 5, pages: 1322-1325, 2011.[11] J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proc. IEEE Int.Conf. Neural Networks, vol. IV, Perth, Australia, 1995, pp. 1942-1948.[12] Eberhart, RC and Kermedy, J. "A new optimizer using particle swarm theory", Proc. Sixth International Symposium on Micromachines and Humanities (Nagoya, Japan), IEEE Service Center, Pkcataway, NJ, 39-43, 1995.[13] X. Xiong and Z. Wan, “The simulation of inverted double pendulum control based on LQR particle swarm optimization algorithm,” IEEE International Conference on Software Engineering and Service Sciences (ICSESS) , pp. 253-256, 2010.[14] M. Marinaki, Y. Marinakis, GE Stavroulakis, “Beam vibration control with piezoelectric sensors and actuators using particle swarm optimization,” Expert Systems with Applications, vol. 38, no. 6, pp... 6872- 6883, 2011.