Runfan Zhang

Synchronization between integer-order chaotic systems and a class of fractional-order chaotic systems via sliding mode control

In this paper, we focus on the synchronization between integer-order chaotic systems and a class of fractional-order chaotic system using the stability theory of fractional-order systems. A new sliding mode method is proposed to accomplish this end for different initial conditions and number of dimensions. More importantly, the vector controller is one-dimensional less than the system. Furthermore, three examples are presented to illustrate the effectiveness of the proposed scheme, which are the synchronization between a fractional-order Chen chaotic system and an integer-order T chaotic system, the synchronization between a fractional-order hyperchaotic system based on Chens system and an integer-order hyperchaotic system, and the synchronization between a fractional-order hyperchaotic system based on Chens system and an integer-order Lorenz chaotic system. Finally, numerical results are presented and are in agreement with theoretical analysis.

No-chattering sliding mode control chaos in Hindmarsh-Rose neurons with uncertain parameters

A Hindmarsh-Rose (HR) model was constructed from voltage clamp data to provide a simple description of the patterned activity seen in molluscan neurons. Its complex dynamics characters are presented, including the phase trajectory, the Lyapunov exponents and the Poincare map. Furthermore, a no-chattering sliding mode control method for the Hindmarsh-Rose (HR) model with uncertain parameters and bounded external disturbances is proposed, and it can control the system to any point and any periodic orbit. Both the theoretical analysis and the simulation results are presented to confirm the validity of the control method.

Synchronization and anti-synchronization of fractional dynamical networks

The issue of synchronization between dynamical systems has attracted much attention, and the systems with integer-order dynamical networks have been well studied. The synchronous behavior of fractional-order dynamical systems is very interesting and importance, but has rarely been studied. In this paper, we studied the synchronization and anti-synchronization behavior between integer-order dynamical networks and fractional-order dynamical systems via a Takagi-Sugeno fuzzy model. Remarkably, there is synchronous behavior in such a system, and this is dramatically different from the behavior of integer-order dynamical networks. Moreover, we studied the impact of different coupling strengths on the dynamical process of synchronization and robustness of the designed controller to different coupling functions, different dimensions of dynamical equations and different fractional orders. Finally, we propose the theoretical analysis, which coincides well with the numerical simulations of five typical examples.

Control and Synchronization of Chaos in RCL-Shunted Josephson Junction with Noise Disturbance Using Only One Controller Term

This paper investigates the control and synchronization of the shunted nonlinear resistive-capacitive-inductance junction (RCLSJ) model under the condition of noise disturbance with only one single controller. Based on the sliding mode control method, the controller is designed to eliminate the chaotic behavior of Josephson junctions and realize the achievement of global asymptotic synchronization of coupled system. Numerical simulation results are presented to demonstrate the validity of the proposed method. The approach is simple and easy to implement and provides reference for chaos control and synchronization in relevant systems.

Nonlinear Predictive Control of a Hydropower System Model

A six-dimensional nonlinear hydropower system controlled by a nonlinear predictive control method is presented in this paper. In terms of the nonlinear predictive control method; the performance index with terminal penalty function is selected. A simple method to find an appropriate terminal penalty function is introduced and its effectiveness is proved. The input-to-state-stability of the controlled system is proved by using the Lyapunov function. Subsequently a six-dimensional model of the hydropower system is presented in the paper. Different with other hydropower system models; the above model includes the hydro-turbine system; the penstock system; the generator system; and the hydraulic servo system accurately describing the operational process of a hydropower plant. Furthermore, the numerical experiments show that the six-dimensional nonlinear hydropower system controlled by the method is stable. In addition, the numerical experiment also illustrates that the nonlinear predictive control method enjoys great advantages over a traditional control method in nonlinear systems. Finally, a strategy to combine the nonlinear predictive control method with other methods is proposed to further facilitate the application of the nonlinear predictive control method into practice.

Anti-synchronization for a class of multi-dimensional autonomous and non-autonomous chaotic systems on the basis of the sliding mode with noise

This paper focuses on anti-synchronization for a class of chaotic systems with noise on the basis of the sliding mode control strategy. In order to achieve this target, a proportional integral surface is proposed to simplify the task of assigning the performance of the error system in sliding motion. We use fewer control items but realize a globally and exponentially asymptotical anti-synchronization. Furthermore, three typical examples are presented: a three-dimensional (3D) autonomous chaotic system, a 4D autonomous chaotic system and a 5D non-autonomous chaotic system. Finally, simulation results are demonstrated for multi-dimensional chaotic systems to illustrate the effectiveness of the proposed scheme.

Controllability of fractional-order directed complex networks

This paper is a step forward to generalize the fundamentals of the conventional controllability in fractional-order complex networks. First, we discuss the existence of controllability theory of fractional-order complex networks. Furthermore, we propose stringent mathematical expression and controllable proof of fractional complex networks. Finally, three typical examples from the simplest network, the chain fractional-order network, to the Small-World network are presented to validate the correctness of the above theorem.