Contribution à l’implémentation de nouvelles approches de synchronisation hybride des systèmes chaotiques à paramètres incertains

Abstract

The aim of the thesis is to consider the performance of some control methods towards the problem of hybrid synchronization of uncertain chaotic systems. These systems are interesting due to the sensitive dependence on initial conditions or what is called the butterfly effect; this feature makes chaotic systems exhibit random behavior. Therefore, the synchronization of chaotic systems with uncertain parameters is an attractive problem, especially in the field of secure communication, that has been intensively studied in the last two decades. The problem of uncertainties on the parameters, in the field of nonlinear control systems, has been solved especially when advanced control methods are used. However, the effect of synchronization of two chaotic systems with uncertain parameters and hybrid synchronization type on some advanced control method is still questionable. The thesis is composed of three main points, each of them dealing with the studied problem from a different aspect. In the first point, we considered the performance of adaptive synchronization in which selftuning adaptive control and active control method are used. This approach has been used intensively to solve the studied problem, but many problems have been reported, and one of the problems is the wrong estimation of the unknown parameters. This problem occurs when two identical or partially identical chaotic systems are synchronized in which the synchronization prevents the adaptation laws to estimate the true values of the unknown parameters. This problem is considered in chapter 2 of the thesis in which we explained the problem, gave the proposed solutions, and the contribution. In the second point, predictive control, particularly generalized predictive control (GPC), has been considered. This approach is sort of complex control method in which the accuracy of the model plays a vital role during the control process. Therefore, we examined, in chapter 3, the performance of GPC towards the studied problem. This chapter consists of two parts. Part one focuses on GPC based on fuzzy PID controllers in which we discussed the roll of the linear model. Part two investigates the performance of GPC based on a neural network model (NNGPC). In the first point and the second point, the synchronization type used is complete synchronization. Therefore, in the third point (chapter 4), we addressed the problem of hybrid synchronization of uncertain chaotic systems in which we investigated the performance of the studied control methods. In general, the effect of synchronization or hybrid synchronization of uncertain chaotic systems on some advanced control methods is partial. The field of chaos synchronization using feedback control is an independent field of research, but the performance of studied methods may not be satisfying when the field of secure communication is involved.