Controller Design Of Uncertain Chaotic Systems And Its Applications In Secure Communication

Research on chaos is one of the important achievements in nonlinearscience. Chaotic motion is a complex motion, whose equation is certain but thetrajectory of the orbits is stochastic. The dynamic characters of chaotic motionhave been proved theoretic significance in describing and quantifying manycomplex phenomena. There are lots of chaotic phenomena in real world. Foroddities of chaos, uncontrolled chaos will not be applied, so chaos control isthe first step of chaos application. Chaos control and chaos application havealready become hot field in nonlinear science. Along the controllers design foruncertain chaotic systems, the main results of this thesis are expressed asfollows:(1) The problem of both the estimation of unknown parameters of thedrive oscillator and the synchronization of two chaotic systems are studied. Weresearch the parameter identification for parameter uncertain chaotic systemsby optimization and adaptive method. A variable structure control design foruncertain chaotic systems subject to sector nonlinear inputs is also considered.(2) We developed the Backstepping based control design for a class ofchaotic systems in strict-feedback form with arbitrary uncertainty. Thedevelopment is able to eliminate the problem of "explosion of complexity"inherent in the existing method. Two designs of this method are presented. Inaddition, the stability analysis is given to show our control law can make thetracking error arbitrarily small.(3) A robust sliding mode observer is proposed and applied to realize thesynchronization for a class of uncertain chaotic systems. The robust outputsliding mode observer is designed by using a sliding mode and a controlstrategy, which is robust to the mismatched time-varying uncertainties in thelinear part of the chaotic systems.(4) The resilient control for uncertain chaotic systems was consideredbased on its T-S fuzzy model. In this section, the uncertainties or perturbationdo not only exist in chaos itself but also in the controller. When taking thefuzzy resilient control design to applications on secure communications, therobust performance is presented by simultaneously considering the effects ofexternal and internal disturbances. Both the continuous-time and thediscrete-time fuzzy chaotic secure communication systems are designed.