Chaos Synchronization Research Of Sliding Mode Control Method Based On LMI

Chaos is a very complex form of motion that exists in nature,which has some random rules.In the field of nonlinear dynamics,chaos control and synchronization are concerned.In order to improve the system performance,chaos in the system must be controlled so that the system behavior can be predicted according to the expected target.Since chaos is essentially non-linear,most chaotic systems inherently contain unknown nonlinear or uncertain parameters.Due to the simple design of sliding mode variable structure control method and strong robustness,the sliding mode control is applied to the synchronization study of uncertain chaotic systems.And because the linear matrix inequality(LMI)technology has simple structure,convenient application and convenient solution,it has been applied to sliding mode control technology in recent years.In this paper,the synchronization of uncertain chaotic systems is realized by using LMI based sliding mode control method for mismatched uncertain chaotic systems.First for a class of uncertain chaos systems with external disturbance is not matching the finite time synchronization problems,combined with linear matrix inequality(LMI)technique and the sliding mode variable structure control method,Lorenz system and chua's circuit,for example,integral switching controller was designed,the finite time synchronization of such a system.In the sliding mode surface design,the design method of integral sliding mode surface is introduced in use of Lyapunov stability theorem,in the form of linear matrix inequality(LMI)gives a sufficient condition for the existence of the sliding mode,and design the controller,the system state matrix of the matched uncertainties and external disturbance.Finally,the LMI tool is used to solve LMI to obtain the design parameters,and the experimental results show that the method has good robustness and anti-interference in the synchronization control of uncertain chaotic systems.Then,based on the third chapter,a sliding mode surface design method based on linear matrix inequality(LMI)is presented,which is applied to the synchronization control of uncertain chaotic system.The uncertainty of the dynamic error system is not determined in the state matrix and input matrix,and the interference factors of the system input are considered.In this paper,the sufficient condition of sliding mode is given by LMI,and an integral sliding mode control design algorithm is proposed and the LMI characteristic of linear sliding mode is presented.Because our approach is LMI based,it provides design flexibility that combines various LMI performance constraints.The existence condition of LMI of sliding surface is given.Finally,the simulation study of Chen chaotic system and Lu chaotic system shows the effectiveness of this method.