Control Of MWR Chaotic Chemical Reaction Model With Uncertain Parameters

Chaos control problem exists in many fields of natural science and social science.To control chaos is to change the chaotic behaviors of the system to approximate or show equilibrium or period state effectively.In this paper,the problems on control of Minimal Willamowski-Rossler(MWR)chemical chaotic systems with the uncertain parameters are discussed.First of all,the robust adaptive control law and parameter estimation for MWR system with uncertain parameters are presented,together with a sliding surface,to control the system to reach the sliding surface and further to be asymptotically stable.Secondly,sufficient condition on F-M synchronization of two chaotic systems with uncertain parameters is put forward.Based on it,in view of two MWR systems with uncertain parameters,a differentiable function and a matrix function are given,and control law and parameter estimation are shown to achieve driver-response system F-M synchronization.Finally,the driver-response system with time-varying parameters is considered,based on the Lyapunov stability theorem,a nonlinear feedback control law is proposed to achieve hybrid projective synchronization of two MWR systems.Matlab numerical simulations are shown to verify the effectiveness of the proposed control strategies.