Control And Synchronization Of The Chaotic Systems Based On The Sliding Mode Variable Structure

Research on chaos is one of the important achievements in nonlinear science. Chaotic motion is a complex motion, whose equation is certain but the trajectory of the orbits is stochastic, there are lots of chaotic phenomena in real world. For oddities of chaos, uncontrolled chaos will not be applied, chaos control is the first step of chaos application, so chaos control and chaos application have already become hot field in nonlinear science.In this paper, we present some techniques for the control and synchronization of chaotic systems from the sliding mode variable structure control theory.(1) Synchronization problem for a class of chaotic systems with external noise disturbances in finite time is analyzed. Dynamic terminal slide mode control is combined with chaos synchronization. Sufficient condition for contructing the dynamic terminal slide mode by introducing nonlinear function into linear slide mode function is given. Corresponding the slide mode controller is given too. The simulation of the synchronization of Duffing system is presented to show the effectiveness of the proposed method.(2) Active sliding mode control is used for a class of uncertain chaos synchronization, so the stability problem of chaotic systems is transformed into sliding mode control problem of linear uncertain systems. The stable sliding surface is designed by using linear matrix inequality (LMI) technique, and reduce the influence of mismatched uncertainties. The sliding mode controller of chaotic systems is derived according to the reaching condition of the sliding mode control.(3) The problem of fuzzy sliding mode control of uncertain chaotic system is studied. Chaotic system is described based on T-S fuzzy models, sliding mode controller is designed, which makes that the state of the system reaches and keeps the proportional-integral sliding mode surface in finite time. Based on this, apply to H∞control, a sufficient condition is proposed in terms of linear matrix inequalities (LMIs) technique and Lyapunov stability theory, which guarantees the sliding mode robust asymptotically stable and has H∞propertiesγ.(4) Slide mode control is combined with fuzzy control, the problem of synchronization control of a class of chaotic systems with uncertainties and external disturbance is studied. The stable sliding surface is designed by using linear matrix inequality (LMI) technique. Then the fuzzy sliding mode controller is designed. The form of the controller is simple and implemented easily. Numerical simulations are provided for illustration and verification of the proposed method. (5) Lastly, according to a class of uncertain time-delay chaotic systems, the fuzzy sliding mode control problem is discussed. There exist mismatched time-varying uncertainties in the systems considered. The conservative feature is overcome in the traditional sliding mode control approach which needs matched uncertainty by nonsingular matrix transformation.