This review article studies some adaptive chaos synchronization methods that were already presented in the literature for a general class of chaotic systems. In this regard, the proposed adaptive controllers and parameter update laws in several papers are inspected, and it is shown that many works suffer from novelty and they can be categorized in a union set.
This paper presents a new general framework for adaptive event-triggered control strategy to extend average inter-event interval, while maintaining the performance of the system. The proposed event-triggering mechanism is acquired from input to state stability conditions, which is defined in terms of system states as well as an adaptation parameter. Under the Lipschitz assumption, a positive lower bound on sampling durations is also established that is essential to restrain the Zeno behavior. Applying the proposed method to linear time-invariant systems, leads to sufficient conditions to guarantee asymptotic stability in the form of matrix inequalities. Moreover, it is shown that there exist more degrees of freedom to improve the performance criterion from theoretical aspects. Finally, in order to show capability of the proposed method and its better performance compared with some recent works, numerical simulations are presented.
Existence of unknown time-delay in the systems is a drastic restriction that it can menace the stability criteria and even deteriorate the performance system. This undesired case would be more intensified if that the uncertain input nonlinearity effects are also considered. To handle the input nonlinearities effects (results in dead-zone and/or hysteresis phenomena) and also unknown time-delay in the chaotic systems, this paper presents an observer-based Model Reference Adaptive Control (MRAC) scheme for a class of unknown time-delay chaotic systems with disturbances. This new method is a delay-independent variable-structure control method which is integrated with an observer system. The main task of the proposed approach is to accomplish a perfect tracking procedure such that unknown parameters are adapted via output estimation error. Furthermore, stability of the closed-loop system is achieved by means of the Lyapunov stability theory. Finally, the proposed methods are applied to some famous chaotic systems to verify the effectiveness of the proposed methods.
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