Research On Control Theory Of Continuous-Time Chaotic Dynamical Systems

Chaotic motion is a complex nonlinear motion, whose trajectory of the orbits hi the phase plane is very complex but not stochastic. We can observe the chaotic phenomenon in a lot of systems. Chaos plays an important role in dynamical systems and is applied hi many fields such as physics, chemistry, economics and so on. The dynamical characters of chaotic motion have been proved to be useful in describing and diagnosing for nonlinear dynamical systems, especially for electronic circuits. 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 and application becomes a new researching focus in nonlinear science fields.The main content of this paper contains the analysis and control of continuous-time chaotic dynamical system. The control theory of chaotic dynamical system mainly contain Learning Control with distal teacher, adaptive state feedback control, sliding-mode synchronous control and passive equivalence control, with which we can realize the stable control of chaotic system. In this dissertation, the main contributions are as following:1. Make an analysis of chaotic dynamical system. We introduced the concepts of chaotic dynamical system and some judging rules whether a system is chaotic. After that, we drew the definitions of Lyapunov exponent, Lyapunov exponent spectrum and the largest Lyapunov exponent. At last we studied the meaning of Lyapunov exponent and the relationship between Lyapunov exponent and eigenvalue of linear system.2. Research on Learning Control with distal teacher of chaotic dynamical system. Analyzed the characters, limitations and application of BP NN, prompted a kind of unproved method, that is Additive-Momentum-Method BP NN. Based on this method, we had a deep study on Learning Control with distal teacher. We adopted object-model-invert system controlling structure. Controllers were formed by proportion control and learning control. The response, the control and the training of BP net consisted of the controlling order. Through theoretical analysis and simulating, we found that the Learning Control with distal teacher of chaotic system had some excellent characters, such as controlling ability, robust ability and so on, which isn't easy to be realized by traditional controlling theories.3. Research on synchronous control theory of uncertain chaotic dynamical system. For the synchronous control of uncertain chaotic dynamical system, two kinds of controller were given, one was state feedback controller, and the other was sliding-mode controller, hi designing the state feedback controller, using adaptive theory, we prompted a kind of adaptive identification method of uncertain parameters and found the way to look after the stabilizing region of controlling system. Using forreference the design method of transverse filer, we presented the way to resolve the control constant, through which we could realize the stabilizing control speedy if initial values of chaotic system was given. In designing the sliding mode controller, adaptive control theory and system identification method were used in system, with which we can realize the synchronous control of uncertain chaotic dynamical system.4. Research on passive equivalence control of chaotic dynamical system. The basic property and the meaning of passive system were introduced firstly. Based on the theory of passive system, we studied the essential conditions, by which chaotic dynamical system was equivalent to passive system. Through theoretic proving, we found that using state feedback could make the passive system stable. Based on passive equivalence theory, we proved that weakly minimum phase nonlinear system and minimum phase nonlinear system transformed by chaotic system having relative degree 1 could be globally asymptotically stabilized by smooth state feedback.