Synchronization of a Class of Chaotic Systems with Different Dimensions

In this paper, two scaling matrices are used to research the synchronization of different dimensional chaotic systems with unknown parameters. Firstly, the definition of synchronization of chaotic systems with different dimensions is introduced. Secondly, based on Lyapunov stability theorem and adaptive control method, an adaptive feedback hybrid controller and parameter adaptive laws are designed to realize synchronization of uncertain chaotic systems with different dimensions. Finally, three numerical experiments are carried out to verify the effectiveness of the proposed method.

An Integral Sliding Mode Control of Uncertain Chaotic Systems via Disturbance Observer

This paper proposes an integral sliding mode control (ISMC) method of a class of uncertain chaotic systems with saturation inputs. Firstly, fuzzy logic system (FLS) is used to estimate the unknown nonlinear function. Then, a disturbance observer is constructed to estimate a compound disturbance, which contains the external disturbance, the error of saturation input and control output, and the fuzzy estimation error. Subsequently, a proposed integral sliding mode controller can ensure that all signals of the closed-loop system are ultimately bounded, and based on the dynamic system of the integral sliding mode variable itself, the ultimate bound of the tracking error can be estimated. Simulation results show that the proposed ISMC method is more effective than the traditional ISMC method.

Robust Adaptive Synchronization of a Class of Uncertain Chaotic Systems with Unknown Time-Delay

In this paper, a robust adaptive control strategy is proposed to synchronize a class of uncertain chaotic systems with unknown time delays. Using Lyapunov theory and Lipschitz conditions in chaotic systems, the necessary adaptation rules for estimating uncertain parameters and unknown time delays are determined. Based on the proposed adaptation rules, an adaptive controller is recommended for the robust synchronization of the aforementioned uncertain systems that prove the robust stability of the proposed control mechanism utilizing the Lyapunov theorem. Finally, to evaluate the proposed robust and adaptive control mechanism, the synchronization of two Jerk chaotic systems with finite non-linear uncertainty and external disturbances as well as unknown fixed and variable time delays are simulated. The simulation results confirm the ability of the proposed control mechanism in robust synchronization of the uncertain chaotic systems as well as to estimate uncertain and unknown parameters.