Control of chaotic systems with uncertain parameters and stochastic disturbance by LMPC

For the chaotic systems with uncertain parameters and stochastic disturbance, in order to satisfy some optimal performance index when chaos control is achieved, the Lyapunov-based model predictive control (LMPC) is introduced. The LMPC scheme is concerned with an auxiliary controller which is constructed in advance. Based on the auxiliary controller and stochastic stability theory, it is shown that the chaotic systems with uncertain parameters and stochastic disturbance are practical stable. With the help of the auxiliary controller, the stability of LMPC can be guaranteed as well as some optimality property. As an example, the unified chaotic system with uncertain parameter and stochastic disturbance is considered and simulation results show the effectiveness of the proposed method.