# Linear Quadratic Optimal Control System Design Using Evolutionary Algorithms

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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 isn’t direct relationship between weighting matrices and control system characteristics and selecting these matrices is done using by 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 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.
Introduction
In designing of many systems and solving the problems, we need to choose an answer between some possible answers as an optimal response. But because of the wide range of answers, all of them cannot be tested and then this test should be performed stochastically. On the other hand, this stochastic procedure should lead to the best answer [1].
Because of its simple implementation in engineering problems, it has been paid special attention on linear quadratic optimal control theory. Linear quadratic optimal control is significant for modern control theory and it can be implemented easily for engineering applications and it is the basic theory of other control techniques. However, in a special case which the cost function is a linear quadratic function, the o...

... middle of paper ...

...o. 5, pp: 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, R. C., and Kermedy, J. “A New Optimizer Using Particles Swarm Theory,” Proc. Sixth International Symposium on Micro Machine and Human Science(Nagoya, Japan), IEEE Service Center, Pkcataway, NJ, 39-43, 1995.
[13] X. Xiong and Z. Wan , "The simulation of double inverted pendulum control based on particle swarm optimization LQR algorithm," IEEE International Conference on Software Engineering and Service Sciences (ICSESS), pp. 253- 256, 2010.
[14] M. Marinaki, Y. Marinakis, G. E. Stavroulakis, "Vibration control of beams with piezoelectric sensors and actuators using particle swarm optimization," Expert Systems with Applications, vol. 38, no. 6, pp. 6872- 6883, 2011.

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