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Controlling (or ordering) chaos is a new concept, which has recently drawn much attention from the communities of engineering, physics, chemistry, biomedical sciences and mathematics. This paper offers an overview of the different interpretations and approaches in the investigation of controlling chaos for various nonlinear dynamical systems. Relevant historical background is provided, several successful techniques are described and analyzed with necessary verifications, and some realistic yet instructive examples are included. The paper also aims at promoting more efforts to be devoted to this challenging and promising new direction of research, as well as its potential applications in nonlinear systems science and engineering.

In this paper, some interesting analysis and simulations on the control of chaotic dynamic systems using conventional feedback control strategies are presented. The typical discrete-time chaotic Lozi system is investigated in some detail. The trajectories of the chaotic Lozi system are controlled to its equilibrium points using conventional feedback controls. Analysis on the design of the feedback controllers and its computer simulations are included.

An adaptive feedback controller is developed based on rigorous Lyapunov argument for an uncertain chaotic Duffing oscillator, in which the three key system parameters are essentially unknown. The proposed method can be easily extended to handle some other chaotic dynamical systems with mild modifications. Simulation results are included to verify the control theory and controller design method.