Xiaoyi Ma

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.

A New Fractional-Order Chaotic System and Its Synchronization with Circuit Simulation

A new fractional-order chaotic system is proposed in this paper, and a list of state trajectories is presented with fractional derivative of different areas. Furthermore, a circuit diagram is studied to realize the fractional-order chaotic system. The new fractional-order chaotic system can be controlled to reach synchronization based on the nonlinear control theory, and the results between numerical emulation and circuit simulation are in agreement with each other.

Nonlinear dynamic analysis for a Francis hydro-turbine governing system and its control

Abstract In this paper, we introduce a novel model of a hydro-turbine system with the effect of surge tank based on state-space equations to study the nonlinear dynamical behaviors of the hydro-turbine system. The critical points of Hopf bifurcation and the relationship of the stability satisfying with the adjustment coefficients are obtained from direct algebraic criterion. Furthermore, the bifurcation diagrams and Lyapunov exponents are presented and analyzed. The dynamical behaviors of the points with representative characteristics are identified and studied in detail. Both theoretical analysis and numerical simulations show that chaotic oscillations, which cannot stabilize the system, may occur with the changes of adjustment coefficients. To control the undesirable chaotic behaviors in this system, fuzzy sliding mode governor based on the sliding mode control (SMC) and the fuzzy logic are designed, and considering the bounded disturbance. Finally, series of numerical simulations are presented to verify the effectiveness of the proposed governor, which prove that the hydro-turbine governing system can maintain a better operation station under the designed governor.

Circuit implementation and model of a new multi-scroll chaotic system

In this paper, a multi-scroll chaotic system from the improved Chuas system is proposed. Moreover, non-linear dynamics are analyzed including phase-space trajectories, bifurcation diagrams, Poincare maps and so on. The most important thing is that we discovered phase-space trajectories, bifurcation diagrams and Poincare maps are unified and closely related, which can describe different aspects of the multi-scroll chaotic system. Furthermore, the corresponding improved module-based circuits are designed for realizing two to four-scroll chaotic attractors, and the experimental results are also obtained, which are consistent with the numerical simulations. Copyright

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 for a class of four-dimensional chaotic systems with random-varying parameters and noise disturbance

This paper investigates the control of a class of four-dimensional chaotic systems with system parameters varying randomly under the condition of noise. Based on the sliding mode control method, the controller is designed to eliminate the chaotic behavior of a system and realize its stabilization. Numerical simulations are presented to demonstrate the validity of the proposed method. The approach proposed in this paper is simple and easy to implement and also provides reference for chaos control in relevant systems.

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.

Synchronization and Antisynchronization of a Class of Chaotic Systems With Nonidentical Orders and Uncertain Parameters

In this paper, we study the synchronization of a class of uncertain chaotic systems. Based on the sliding mode control and stability theory in fractional calculus, a new controller is designed to achieve synchronization. Examples are presented to illustrate the effectiveness of the proposed controller, like the synchronization between an integer-order system and a fraction-order system, the synchronization between two fractional-order hyperchaotic systems (FOHS) with nonidentical fractional orders, the antisynchronization between an integer-order system and a fraction-order system, the synchronization between two new nonautonomous systems. The simulation results are in good agreement with the theory analysis and it is noted that the proposed control method is of vital importance for practical system parameters are uncertain and imprecise.