Practical Explicit Model Predictive Control for a Class of Noise-embedded Chaotic Hybrid Systems

Controlling a class of chaotic hybrid systems in the presence of noise is investigated in this paper. To reach this goal, an explicit model predictive control (eMPC) in combination with nonlinear estimators is employed. Using the eMPC method, all the computations of the common MPC approach are moved off-line. Therefore, the off-line control law makes it easier to be implemented in comparison with the on-line approach, especially for complex systems like the chaotic ones. In order to verify the proposed control structure practically, an op-amp based Chua's chaotic circuit is designed. The white Gaussian noise is considered in this circuit. Therefore, the nonlinear estimators -extended and unscented Kalman filter (EKF and UKF)- are utilized to estimate signals from the noise-embedded chaotic system. Performance of these estimators for this experimental setup is compared in both open-loop and closed-loop systems. The experimental results demonstrate the effectiveness of the eMPC approach as well as the nonlinear estimators for chaos control in the presence of noise.