Control And Synchronization Of Chaos Via Fuzzy Neural Network

Chaos is a special feature of complex nonlinear dynamics systems. It has the random-like behavior usually seen in stochastic systems although it is associated with deterministic dynamics. Chaos is at the edge of stability and therefore could easily lead systems to an unstable, performance-degraded, or even catastrophic situation. In such cases, chaos is considered as undesired and should be totally avoided or completely eliminated.Given that most physical chaotic systems inherently contain unknown nonlinearities or uncertain parameters, this dissertation is concerned with the robust and adaptive control for uncertain and unknown chaotic systems. The methodology of fuzzy neural network (FNN) is adopted to develop effective nonlinear adaptive control approaches for chaos control.For designing a robust control, sliding mode control is frequently adopted due to its inherent advantages of easy realization, fast response, good transient performance and insensitive to variation in plant parameters or external disturbances. In the face of unknown chaotic systems, FNN is incorporated into the Lyapunov stability theory in an adaptive way. The main achievements contained in the research are as follows:Firstly, controlling uncertain multi-scroll critical chaotic systems is studied. According to variable structure control theory, the sliding mode controller of the uncertain multi-scroll critical chaotic system is designed, which containing sector nonlinearity and dead zone inputs. For an arbitrarily given initial states of the uncertain multi-scroll chaotic system, the global stabilizing for the equilibrium point or external reference signal is achieved.Secondly, tracking control for multi-scroll chaotic system is studied. Based on FNN compensator, tracking control for multi-scroll chaotic system from saturated function series is designed. Under the FNN nonlinear compensator, the resulting system is then dominated by the linear part, with some or weak residual nonlinearity. Thus, a linear state feedback controller can be proposed, to drive the multi-scroll chaotic system to the given reference signals.Thirdly, based on observer theory and self-structuring fuzzy neural network (SFNN) system indentification, an observer-based fuzzy neural sliding control (OFNSMC) scheme for interconnected unknown chaotic systems is developed. The OFNSMC system is composed of a computation controller and a robust controller, and the L2 tracking performance is achieved. Fourthly, based on dynamic fuzzy neural network (DFNN) modeling and backstepping control method, A simple and systematic approach is developed for modeling and neural adaptive backstepping control of an uncertain chaotic system. The DFNN works through structure and parameter-learning phases for adaptation, which implements Takagi-Sugeno-Kang fuzzy system based on extended radial basis function (RBF) neural networks.Fifthly, the problem of synchronization of uncertain chaotic systems with random-varying parameters is investigated. A self-organizing adaptive neural control (SAFNC) for the synchronization of uncertain chaotic systems with random-varying parameters is designed.