Narrow Results

This paper concerns the design of an observer-based repetitive control system (RCS) to improve the periodic disturbance rejection performance. The periodic disturbance is estimated by a repetitive learning based estimator (RLE) and rejected by incorporation of the estimation into a repetitive control (RC) input. Firstly, the configuration of the observer-based RCS with the RLE is described. Then, a continuous–discrete two-dimensional (2D) model is built to describe the RCS. By choosing an appropriate Lyapunov functional, a sufficient condition is proposed to guarantee the stability of the RCS. Finally, a numerical example is given to verify the effectiveness of the proposed method.

In this paper, a time-delayed chaos control method based on repetitive learning is proposed. A general repetitive learning control structure based on the invariant manifold of the chaotic system is given. The integration of the repetitive learning control principle and the time-delayed chaos control technique enables adaptive learning of appropriate control actions from learning cycles. In contrast to the conventional repetitive learning control, no exact knowledge (analytic representation) of the target unstable periodic orbits is needed, except for the time delay constant, which can be identified via either experiments or adaptive learning. The controller effectively stabilizes the states of the continuous-time chaos on desired unstable periodic orbits. Simulations on the Duffing and Lorenz chaotic systems are provided to verify the design and analysis.

In this paper, a learning control approach is applied to the synchronization of two uncertain chaotic systems which contain both time varying and time invariant parametric uncertainties. The new learning approach also deals with unknown time varying parameters having distinct periods in the master and slave systems. Using the Lyapunov–Krasovskii functional and incorporating periodic parametric learning mechanism, the global stability and asymptotic synchronization between the master and the slave systems are obtained. Simulations on a representative class of chaotic systems show the effectiveness of the method.