The Control, Synchronization And Its Application Of Unified Model Chaotic System

Chaotic motion is a complex nonlinear motion, whose trajectory of the orbits in the phase plane is very complex but not stochastic. We can observe the chaotic phenomenon in a lot of systems. The dynamic properties of chaos signal such as ergodicity, aperiodic, uncorrelated, broad band and noise-like have been proved to be useful for communication and picture encrypt systems and in describing and diagnosing nonlinear dynamic systems. Chaos plays an important role in dynamical systems and is applied in many fields such as physics, chemistry, economics and so on. The sensitivity to changes in initial conditions, a kind of intrinsically character, and complexity of chaotic dynamical system make the research on the chaotic control theory to be more challenging. Research on chaotic control, synchronization and its application becomes a new researching focus in nonlinear science fields.The main content of this paper contains the analysis and control of unified chaotic dynamical system. The control theory of chaotic control, synchronization system mainly contains passive control, adaptive state feedback control, sliding-mode synchronous control, and so on. In this dissertation, the main contributions are as follows:1. Based on the nonlinear function of unified chaotic system satisfies Lipschitz condition, the synchronization error system for the drive system and the response system is given and the problem to make system synchronize can be transformed to ensure the global approximate stability of the synchronization system. An adaptive passivity method is adopted to design statement feedback controller to ensure the global stability of the synchronization system. With this method, the unified system can be synchronized with different initial conditions. The simulation results show the validity of the method.2. The passive synchronization method of unified chaotic system with uncertain parameters is studied. Based on the method of steepest descent, the uncertain parameters can be identified adaptively. Through making the unified chaotic system be a passive system, the synchronization controller is designed with the uncertain parameters, and the synchronization error system of unified chaotic system can be stabilized. The simulation results show that the control method is effective for unified chaotic system synchronization.3. A synchronization control approach for unified chaotic system with uncertainties and time delay is presented using passive control theory. The stability of the synchronization error system is studied so that the unified chaotic system can be synchronized with uncertainties and channel time delay. Because the chaotic trajectory is limitary and the nonlinear function of the unified chaotic system satisfies Lipschitz condition, the error system transformed by synchronization error system can be globally asymptotically stabilized by state feedback, therefore it implements the synchronization control of unified chaotic system with uncertainties and time delay. Simulation results show that the adaptive passive synchronization scheme is efficient, and the generalized synchronization can also be realized.4. The equivalent passive control theory for fractional order unified chaotic system is studied. The chaotic behaviors in the fractional order unified system are numerically investigated. On the unstable equilibrium point, it is used the "equivalent passivity" method of nonlinear control design to derive the nonlinear controller. How to choose the control parameter is also studied so that the controller is to stabilize the output chaotic trajectory by driving it to the nearest equilibrium point in the basin of attraction. With Laplace transform theory, the equivalent integer order state equation from fractional order nonlinear system is gotten, and the statement output can be solved.5. The stability of fractional order unified chaotic system is studied with sliding mode control theory. The sliding manifold is constructed by the definition of fractional order derivative and integral for fractional order unified chaotic system. It is proved that the sliding manifold exists. In order to improve the convergence rate, the controller includes two parts:continuous controller and switching controller. According to the boundness of chaotic attractor, the chosen values of the controlling parameters are decided by parameters inequality. Simulation results are obtained to verify the effectiveness of this method.