Unified linear time-invariant model predictive control for strong nonlinear chaotic systems

It is well known that an alone linear controller is difficult to control a chaotic system, because intensive nonlinearities exist in such system. Meanwhile, depending closely on a precise mathematical modeling of the system and high computational complexity, model predictive control has its inherent drawback in controlling nonlinear systems. In this paper, a unified linear time-invariant model predictive control for intensive nonlinear chaotic systems is presented. The presented model predictive control algorithm is based on an extended state observer, and the precise mathematical modeling is not required. Through this method, not only the required coefficient matrix of impulse response can be derived analytically, but also the future output prediction is explicitly calculated by only using the current output sample. Therefore, the computational complexity can be reduced sufficiently. The merits of this method include, the Diophantine equation needing no calculation, and independence of precise mathematical modeling. According to the variation of the cost function, the order of the controller can be reduced, and the system stability is enhanced. Finally, numerical simulations of three kinds of chaotic systems confirm the effectiveness of the proposed method

Persistence of nonautonomous logistic system with time-varying delays and impulsive perturbations

In this paper, we develop the impulsive control theory to nonautonomous logistic system with time-varying delays. Some sufficient conditions ensuring the persistence of nonautonomous logistic system with time-varying delays and impulsive perturbations are derived. It is shown that the persistence of the considered system is heavily dependent on the impulsive perturbations. The proposed method of this paper is completely new. Two examples and the simulations are given to illustrate the proposed method and results

On the Practical Stability of Impulsive Differential Equations with Infinite Delay in Terms of Two Measures

We consider the practical stability of impulsive differential equations with infinite delay in terms of two measures. New stability criteria are established by employing Lyapunov functions and Razumikhin technique. Moreover, an example is given to illustrate the advantage of the obtained result

Impulsive Control for the Synchronization of Chaotic Systems with Time Delay

This paper considers impulsive control for the synchronization of chaotic systems with time delays. Based on the Lyapunov functions and the Razumikhin technique, some new synchronization criteria with an exponential convergence rate are derived. Our results show that impulses do contribute to globally exponential synchronization of dynamical systems. Besides, the impulsive moments are independent of the upper bound of time delays. Furthermore, a bigger upper bound of impulsive intervals for the synchronization of chaotic systems can be obtained when compared with many previous studies. Hence, our results are less conservative and more effective for the synchronization analysis. A numerical example is given to show the validity and potential of the developed results