Zhao Guang-zhou

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.

Sliding mode control for synchronization of chaotic systems with structure or parameters mismatching

This paper deals with the synchronization of chaotic systems with structure or parameters difference. Nonlinear differential geometry theory was applied to transform the chaotic discrepancy system into canonical form. A feedback control for synchronizing two chaotic systems is proposed based on sliding mode control design. To make this controller physically realizable, an extended state observer is used to estimate the error between the transmitter and receiver. Two illustrative examples were carried out: (1) The Chua oscillator was used to show that synchronization was achieved and the message signal was recovered in spite of parametric variations; (2) Two second-order driven oscillators were presented to show that the synchronization can be achieved and that the message can be recovered in spite of the strictly different model.

Control of discrete chaotic systems with uncertain parameters

A new chaos control method, the parametric adaptive open-plus-closed-loop control (PAOPCL), is developed for stabilizing the discrete chaotic system, in which parameters are uncertain and can not be directly measured, by estimating the real parameters using double observers. First, the open-plus-closed-loop control (OPCL) is recalled and studied and the condition is presented, in which OPCL can control the chaotic system when the parameters can be obtained directly. Finally, the effectiveness of the proposed approach is illustrated by stabilizing the chaotic dynamics of the logistic map and the Henon map.