Class Of Fractional-order Hyperchaotic Systems Research Articles

Synchronization of uncertain fractional-order hyper-chaotic systems via a novel adaptive interval type-2 fuzzy active sliding mode controller

In this paper, a novel adaptive interval type-2 fuzzy active sliding mode control (AIT2FASMC) approach is proposed for synchronization of fractional-order hyper-chaotic systems. The synchronization is achieved in front of uncertainties facing the fuzzy logic controller (FLC) in fractional–order hyper-chaotic systems such as uncertainties in control outputs, uncertainties in inputs to the fuzzy logic controller, and linguistic uncertainties. Two fractional-order hyper-chaotic systems can be synchronized based on Lyapunov stability theorem by using direct AIT2FASMC approach. Also, the proposed method reduces the chattering phenomena in the control signal, significantly. This novel fractional-order sliding mode controller is proposed for robust stabilization/synchronization problem of a class of fractional-order hyper-chaotic systems in the presence of external noise. Type-2 fuzzy active sliding mode control \(\left( {FASMC}\right) \) have the ability to overcome the limitations of type-1 FASMC when system is corrupted by high levels of uncertainty. Finally, the proposed approach is applied to two identical and non-identical fractional-order hyper-chaotic systems when the slave system is perturbed by external noise. Simulation results show applicability and feasibility of the proposed finite-time control strategy.

Synchronizing a class of uncertain and variable time-delay fractional-order hyper-chaotic systems by adaptive sliding robust mode control

In view of a class of synchronization problems about uncertain and variable time-delay systems, this paper puts forward a method of adaptive sliding robust control. Based on the Lyapunov stability theory and adaptive sliding mode control methods, the adaptive sliding robust controllers and the parameter adaptive rate are designed. A single controller designed by the synchronous control method is applicable to the synchronizing of a class of fractional-order hyper-chaotic systems, and it has a great ability to resist noise-perturbed. What is more, it can also well control the time-varying time-delay systems. So the controller is of highly practical value. Furthermore, by introducing a certain amount of compensation into the system, the influences of the uncertainty and the noise-disturbance can be eliminated, thus the synchronization of the uncertainty fractional-order hyper-chaotic system is realized. In addition, the control of the synchronous errors of the systems can be stable in arbitrarily small domain. Finally, time-varying and time-delay fractional-order Chen's hyper-chaotic systems with the external noisy disturbances and uncertain parameters are numerically simulated, and the effectiveness of the proposed control method is verified.

Robust Synchronization of Fractional-Order Hyperchaotic Systems Subjected to Input Nonlinearity and Unmatched External Perturbations

This paper investigates the robust synchronization problem for a class of fractional-order hyperchaotic systems subjected to unmatched uncertainties and input nonlinearity. Based on the sliding mode control (SMC) technique, this approach only uses a single controller to achieve chaos synchronization, which reduces the cost and complexity for synchronization control implementation. As expected, the error states can be driven to zero or into predictable bounds for matched and unmatched perturbations, respectively, even with input nonlinearity.

Impulsive synchronisation of a class of fractional-order hyperchaotic systems**Project supported by the National Natural Science Foundation of China (Grant Nos. 60573172 and 60973152), the Doctoral Program Foundation of the Institution of Higher Education of China (Grant No. 20070141014) and the Natural Science Foundation of Liaoning Province, China (No. 20082165).

In this paper, an impulsive synchronisation scheme for a class of fractional-order hyperchaotic systems is proposed. The sufficient conditions of a class of integral-order hyperchaotic systems' impulsive synchronisation are illustrated. Furthermore, we apply the sufficient conditions to a class of fractional-order hyperchaotic systems and well achieve impulsive synchronisation of these fractional-order hyperchaotic systems, thereby extending the applicable scope of impulsive synchronisation. Numerical simulations further demonstrate the feasibility and effectiveness of the proposed scheme.