Qi Donglian

Passive control of chaotic system with multiple strange attractors

In this paper we present a new simple controller for a chaotic system, that is, the Newton–Leipnik equation with two strange attractors: the upper attractor (UA) and the lower attractor (LA). The controller design is based on the passive technique. The final structure of this controller for original stabilization has a simple nonlinear feedback form. Using a passive method, we prove the stability of a closed-loop system. Based on the controller derived from the passive principle, we investigate three different kinds of chaotic control of the system, separately: the original control forcing the chaotic motion to settle down to the origin from an arbitrary position of the phase space; the chaotic intra-attractor control for stabilizing the equilibrium points only belonging to the upper chaotic attractor or the lower chaotic one, and the inter-attractor control for compelling the chaotic oscillation from one basin to another one. Both theoretical analysis and simulation results verify the validity of the suggested method.

Passive control of Permanent Magnet Synchronous Motor chaotic systems

Permanent Magnet Synchronous Motor model can exhibit a variety of chaotic phenomena under some choices of system parameters and external input. Based on the property of passive system, the essential conditions were studied, by which Permanent Magnet Synchronous Motor chaotic system could be equivalent to passive system. Using Lyapunov stability theory, the convergence condition deciding the system’s characters was discussed. In the convergence condition area, the equivalent passive system could be globally asymptotically stabilized by smooth state feedback.

Comparison between two different sliding mode controllers for a fractional-order unified chaotic system

Two different sliding mode controllers for a fractional order unified chaotic system are presented. The controller for an integer-order unified chaotic system is substituted directly into the fractional-order counterpart system, and the fractional-order system can be made asymptotically stable by this controller. By proving the existence of a sliding manifold containing fractional integral, the controller for a fractional-order system is obtained, which can stabilize it. A comparison between these different methods shows that the performance of a sliding mode controller with a fractional integral is more robust than the other for controlling a fractional order unified chaotic system.

Mittag-Leffler synchronization of fractional-order uncertain chaotic systems

This paper deals with the synchronization of fractional-order chaotic systems with unknown parameters and unknown disturbances. An adaptive control scheme combined with fractional-order update laws is proposed. The asymptotic stability of the error system is proved in the sense of generalized Mittag–Leffler stability. The two fractional-order chaotic systems can be synchronized in the presence of model uncertainties and additive disturbances. Finally these new developments are illustrated in examples and numerical simulations are provided to demonstrate the effectiveness of the proposed control scheme.

The stability control of fractional order unified chaotic system with sliding mode control theory

This paper studies the stability of the fractional order unified chaotic system with sliding mode control theory. The sliding manifold is constructed by the definition of fractional order derivative and integral for the fractional order unified chaotic system. By the existing proof of sliding manifold, the sliding mode controller is designed. To improve the convergence rate, the equivalent controller includes two parts: the continuous part and switching part. With Gronwalls inequality and the boundness of chaotic attractor, the finite stabilization of the fractional order unified chaotic system is proved, and the controlling parameters can be obtained. Simulation results are made to verify the effectiveness of this method.

Chaotic attractor transforming control of hybrid Lorenz–Chen system

Based on passive theory, this paper studies a hybrid chaotic dynamical system from the mathematics perspective to implement the control of system stabilization. According to the Jacobian matrix of the nonlinear system, the stabilization control region is gotten. The controller is designed to stabilize fast the minimum phase Lorenz–Chen chaotic system after equivalently transforming from chaotic system to passive system. The simulation results show that the system not only can be controlled at the different equilibria, but also can be transformed between the different chaotic attractors.

Adaptive passive equivalence of uncertain Lü system

An adaptive passive strategy for controlling uncertain Lu system is proposed. Since the uncertain Lu system is minimum phase and the uncertain parameters are from a bounded compact set, the essential conditions are studied by which uncertain Lu system could be equivalent to a passive system, and the adaptive control law is given. Using passive theory, the uncertain Lu system could be globally asymptotically stabilized at different equilibria by the smooth state feedback.

Passive control of Permanent Magnet Synchronous Motor chaotic system based on state observer

Passive system theory was applied to propose a new passive control method with nonlinear observer of the Permanent Magnet Synchronous Motor chaotic system. Through constructing a Lyapunov function, the subsystem of the Permanent Magnet Synchronous Motor chaotic system could be proved to be globally stable at the equilibrium point. Then a controller with smooth state feedback is designed so that the Permanent Magnet Synchronous Motor chaotic system can be equivalent to a passive system. To get the state variables of the controller, the nonlinear observer is also studied. It is found that the outputs of the nonlinear observer can approximate the state variables of the Permanent Magnet Synchronous Motor chaotic system if the system’s nonlinear function is a globally Lipschitz function. Simulation results showed that the equivalent passive system of Permanent Magnet Synchronous Motor chaotic system could be globally asymptotically stabilized by smooth state feedback in the observed parameter convergence condition area.

Passive control of a class of chaotic dynamical systems with nonlinear observer

A passive control strategy with nonlinear observer is proposed, which can be used to control a class of chaotic dynamical systems to stabilize at different equilibrium points. If the nonlinear function of chaotic system satisfies Lipschitz condition, the nonlinear observer can observe the state variables of the chaotic systems. An important property of passive system is studied to control chaotic systems, that is passive system can be asymptotically stabilized by state feedback controller whose state variables are presented by nonlinear observer. Simulation results indicated that the proposed chaos control method is very effective in a class of chaotic systems.

Hybrid internal model control and proportional control of chaotic dynamical systems

A new chaos control method is proposed to take advantage of chaos or avoid it. The hybrid Internal Model Control and Proportional Control learning scheme are introduced. In order to gain the desired robust performance and ensure the systems stability, Adaptive Momentum Algorithms are also developed. Through properly designing the neural network plant model and neural network controller, the chaotic dynamical systems are controlled while the parameters of the BP neural network are modified. Taking the Lorenz chaotic system as example, the results show that chaotic dynamical systems can be stabilized at the desired orbits by this control strategy.