The Control of The Lorenz Chaotic System Blended With The Noise

Abstract

In this study, the Lorenz chaotic system behavior is investigated according to the change in the noise of the system and measurement. The noise was emerged as an important impact on the Lorenz chaotic system. The discrete-time LQR (Linear Quadratic Regulator) control method and discrete-time PI controller method have been used to the noisy system controls. Noise was accepted as a destructor that changes the output behavior of the chaotic system. Noisy system outputs were enforced to move to the equilibrium points by the support of controllers. Optimization of the controller parameters for noiseless system models was performed using a genetic algorithm method. Then, both control system algorithms determined as successful in transporting to the equilibrium point for state variables which are blended with the noise. Changes, associated with the noise conditions are given in the graphics and tables. Besides, the error performance criteria and the control performance criteria were obtained to evaluate the results. This study was performed by MATLAB-Simulink simulation program.

Keywords

• Lorenz chaotic system,Gaussian white noise,Discrete-time PI,LQR,controller,Genetic algorithm,Matlab-Simulink

References

1. Lorenz, E. N., Deterministic non periodic flow. J. Atmos. Sci., 20, 130–141, 1963.