Three-Stage-Impulse Control of Memristor-Based Chen Hyper-Chaotic System

Abstract

In this paper, on the basis of the three-dimensional Chen system, a smooth continuous nonlinear flux-controlled memristor model is used as the positive feedback term of this system, a hyper-chaotic circuit system is successfully constructed, and a simulated equivalent circuit is built for simulation using Multisim software, which agrees with the numerical simulation results by comparison. Meanwhile, a new impulsive control mode called the three-stage-impulse is put forward. It is a cyclic system with three components: continuous inputs are exerted in the first and third parts of the cycle while giving no input in the second part of the cycle, an impulse is exerted at the end of each continuous subsystem, the controller is simple in structure and effective in stabilizing most existing nonlinear systems. The Chen hyper-chaotic system will be controlled based on the three-stage-impulse control method combined with the Lyapunov stability principle. At the end of this paper, we have employed and simulated a numerical example; the experimental results show that the controller is effective for controlling and stabilizing the newly designed hyper-chaotic system.

Well-Posedness, Dynamics, and Control of Nonlinear Differential System with Initial-Boundary Value

“…Pulses are applied to each continuous subsystem, and the controller structure is simple. The exponential stability of the hyperchaotic system is achieved, and computer simulation confirms the effectiveness of the algorithm (Figure 9 in [8]). A new Lyapunov functional is proposed in reference [9], which does not require all matrices in the quadratic form of the Lyapunov functional to be positively definite, while the quadratic form remains positively definite, making the estimation more relaxed.…”

“…Chen et al proposed in [7] an uncertain sandwich control system with impulse time windows, which was well displayed in the computer simulations (Figures 2-5 in [7]). Reference [8] reported a new pulse control mode, which is a three-level pulse. It is a cyclic system with three parts: continuous inputs are applied to the first and third parts of the cycle without the second part of the input cycle.…”

“…The series of papers in this Special Issue reflect the application of dynamic system theory in finance, neural networks, and other control systems [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. For example, the authors of [1] studied the stability of PSS in hyperchaotic financial systems.…”

“…In order to make this conclusion more general, the authors of [7] inserted a countable number of pulses during the T period and studied its exponential stability. Additionally, the authors of [8] successfully constructed a hyper-chaotic circuit system on the basis of the three-dimensional Chen system, using the smooth continuous nonlinear flux controlled reluctance model as the positive feedback term of the system, and realized the exponential stabilization of the memristor-based hyper-chaotic system by using the Lyapunov function and linear inequality matrix techniques.…”

“…On the other hand, the stability and synchronization control of dynamic systems are also among the main contents of cybernetics, and they are part of well-posed problems. Fifteen papers [1][2][3][4][5][6][7][8][9][10][11][12][13][14] in this Special Issue deal with the stabilization and synchronization control of initial boundary value problems of partial differential equations or ordinary differential equations, and jointly complete the original work plan of this Special Issue. The papers in this Special Issue can be divided according to the following scheme considering their main purposes:…”