Output-feedback lag-synchronization of time-delayed chaotic systems in the presence of external disturbances subjected to input nonlinearity

In this paper, an adaptive output error feedback control scheme is proposed for the lag-synchronization of two time-delayed chaotic systems in the presence of channel time-delay, external disturbances and input nonlinearity. Using the Lyapunov theory, stability of the proposed adaptive controller is proved. Lyapunov-Krasovskii approach is used to deal with the existence of time-delay in the system dynamics. Finally, two numerical simulations are presented to illustrate the effectiveness of the developed method.     

Simple adaptive output-feedback lag-synchronization of multiple time-delayed chaotic systems

In this letter, a simple adaptive output-feedback controller is designed for lag-synchronization of two multiple time-delayed chaotic systems in the presence of uncertainty, external disturbances, and input nonlinearity. Based on Lyapunov stability theorem and adaptive techniques, sufficient conditions for lag-synchronization of these two systems are achieved. To deal with the existence of unknown time-delays in the system dynamics, the novel Lyapunov-Krasovskii functionals are used. Finally, a numerical simulation is presented to show the effectiveness of the proposed chaos lag-synchronization scheme.     

Observer-based model reference adaptive control for unknown time-delay chaotic systems with input nonlinearity

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.     

Adaptive controller design for lag-synchronization of two non-identical time-delayed chaotic systems with unknown parameters

In this Letter, two adaptive controllers are proposed for the lag-synchronization of two non-identical time-delayed chaotic systems with fully unknown parameters. Based on Lyapunov-stability theorem and adaptive techniques, sufficient conditions for the lag-synchronization of these two systems are discussed. Finally, illustrative examples are given to verify the validity of the developed controllers.     

Iterative sliding mode control

Iterative Learning Control (ILC) methods are described and applied ever-increasingly as powerful tools to control dynamics nowadays.

ILC’s methods in most studies are described as based on repetitive process from the beginning to the end of process or as a kind of repetitive control.

Our newly designed controllers based on a particular case of iterative learning control radically differ from conventional methods in attempting to stabilize a class of non linear systems.

In this paper two kinds of ILC method are introduced in two separate sections. In the first, our newly designed method satisfies the condition of a Lyapunov stability theorem in a class of non linear systems in which their structures have the Lipschitz property. In the second, by freezing the time and moving to a new virtual axis, called the index axis, this newly designed method tries to find the best value for control at this time step and can be used in two modes, on-line and off-line.

In both methods, by satisfying the convergence condition of our designed ILC, closed loop stability is obtained automatically.