Robust Fault-Tolerant Control For A Class Of Chaotic Systems

Since the birth of the chaos synchronization control theory in1990s, the theory hasbeen an unprecedented development. The results of chaotic synchronization control theoryare based on a mathematical model without failure. But in the actual project, due to theinstability of the internal or external factors, a failure always exists. Therefore, design ofthe controller needs fault-tolerant technology, study of chaotic systems with robust faulttolerant control has important theoretical and practical value. In this thesis, utilizing robustcontrol, fault tolerant control and Lyapunov stability theory to study the chaossynchronization and chaos synchronization application. The specific contents are asfollows:The problem of robust non-fragileH fault tolerant synchronization control for aclass of master-slave chaotic systems with multiple time-delays is considered. Firstly,non-fragile controller was designed for the chaotic systems without fault, which ensuredboth the robust stability and prescribed level ofH performance index by Lyapunovstability theory; non-fragile fault-tolerant controller was designed for the fault occurred inchaotic systems with outside interference and pointed out the sufficient conditions for theexistence of controller. The main result is converted into the form of a linear matrixinequality for design controller through the matrix transformation methods, so it isconvenient to obtain the expression of controller; Finally, the simulation example wasgiven through comparing and analyzing, which shows that the method is effective andfeasible.The robust fault tolerant synchronization control scheme is proposed for time delayedRossler chaotic systems with secure information. If the synchronization of chaotic systemsis obtained, the secure information will be efficiently recovered. Firstly, the state observerand the robust controller was designed for the chaotic systems without fault, which ensuredthe synchronization of chaotic systems is obtained and the hidden information can berecovered by Lyapunov stability theory; Secondly, fault-tolerant controller was designedfor the fault occurred in chaotic systems. When the convergence of the synchronization error is achieved, the signal can be recovered. Finally, using two step delayed Rosslersystem for secure communication to sine wave, the result was given through comparingand analyzing, which shows that the method is effective and feasible.The practical problems of a class of chaotic systems in the secure communicationprocess when controller failure was studied in this thesis. First, wavelet transformation isperformed on the image, extracting the approximate component. Then, use theRunge-Kutta method on Rossler chaotic system to generate chaotic sequences, so that thesequence has the same dimension as the image, on this basis, using chaos tolerantalgorithm to encrypt the approximation image matrix, Image has execute only once addoperation. Finally, simulate the algorithm through experiment, fault tolerant encryptalgorithm is simple and effective; the algorithm is able to achieve secure communicationwith good security performance in the case of a controller failure.