Exponential stabilization of nonlinear systems under saturated control involving impulse correction

This paper studies the problem of locally exponential stabilization (LES) of nonlinear systems under a class of hybrid control in the framework of actuator saturation, where the limitation of actuator saturation on both continuous state feedback control and impulsive control are fully considered. Based on impulsive control theory and differential inclusion approach, some sufficient conditions for LES are derived, where a novel set inclusion relation is proposed to handle the double saturation nonlinearities. Different from the existing results that each part of saturated hybrid control (SHC) is required to stabilize the system individually, our results relax the requirement by making full use of the correction effect of the impulse. Moreover, the maximum of estimation of domain of attraction is obtained by a convex optimal problem and corresponding algorithm. The result is applied to the robustness for a class of nonlinear systems. Finally, the validity of the results is shown by two examples and their simulations, where the synchronization problem of Chua’s oscillator is illustrated in the framework of actuator saturation.     

一类非光滑Chua’s电路的同步控制

本文研究两个带x|x|非线性项的Chua’s电路的全局指数同步和全局同步的控制问题.证明这两个系统在未加控制时不可能同步,但设计不同的控制器可以实现这两个系统的全局指数同步和全局同步.     

分数阶Chua's系统错位同步无感模块化电路实现及应用

基于分数阶混沌系统稳定性理论, 设计高效的非线性控制器, 实现初始值不同的两个分数阶Chua's系统错位投影同步. 根据分数阶复频域近似方法, 提出分数阶系统的等效电路, 实现分数阶Chua's系统错位投影同步的无感模块化电路. 最后,利用改进的混沌掩盖通信原理, 将以上同步方案应用于混沌保密通信中, 在发送端使用分数阶混沌序列对有用信号加密传送, 从接收端可以无失真地恢复出有用信号. 数值仿真与电路仿真证实了提出方案的可行性. 关键词： 分数阶Chua's系统 错位投影同步 无感模块化电路 保密通信     

基于单电子器件的混沌电路研究

利用单电子晶体管和金属氧化物半导体的混合器件——SETMOS设计实现了细胞神经网络结构的蔡氏电路,得到了单涡卷吸引子和双涡卷吸引子.通过设计构成的SETMOS跨导放大器和SETMOS电压比较器,提出了基于SETMOS的类双涡卷混沌电路,仿真验证了类双涡卷吸引子.模拟结果表明,所设计的硬件电路结构简单,功耗低,有利于进一步提高集成电路的集成度,为混沌在工程领域的实际应用提供了新方法. 关键词： 细胞神经网络 蔡氏电路 混沌 涡卷     

一个超混沌六阶蔡氏电路及其硬件实现

文章构建了一个新的超混沌六阶蔡氏电路,计算了该系统的Lyapunov指数和维数,给出了系统的数值仿真相图.同时,设计了相应的电子电路并进行了硬件实现,实验结果与仿真结果完全吻合,由此证实了该系统不仅存在而且可物理实现. 关键词： 六阶蔡氏电路 超混沌 硬件实验 混沌发生器     

Localization of hidden Chua?s attractors

The classical attractors of Lorenz, Rossler, Chua, Chen, and other widely-known attractors are those excited from unstable equilibria. From computational point of view this allows one to use numerical method, in which after transient process a trajectory, started from a point of unstable manifold in the neighborhood of equilibrium, reaches an attractor and identifies it. However there are attractors of another type: hidden attractors, a basin of attraction of which does not contain neighborhoods of equilibria. In the present Letter for localization of hidden attractors of Chua?s circuit it is suggested to use a special analytical-numerical algorithm.     

Impulsive stabilization of a class of nonlinear system with bounded gain error

Considering mechanical limitation or device restriction in practical application, this paper investigates impulsive stabilization of nonlinear systems with impulsive gain error. Compared with the existing impulsive analytical approaches,the proposed impulsive control method is more practically applicable, which includes control gain error with an acceptable boundary. A sufficient criterion for global exponential stability of an impulsive control system is derived, which relaxes the condition for precise impulsive gain efficiently. The effectiveness of the proposed method is confirmed by theoretical analysis and numerical simulation based on Chua＇s circuit.     

Chaos synchronization of the Chua system with a fractional order

Chaos synchronization of two identical Chua systems with the same fractional order is studied by utilizing the Pecora–Carroll (PC) method, the active–passive decomposition (PAD) method, the one-way coupling method and the bidirectional coupling one. The sufficient conditions for achieving synchronization between these two systems are derived via the Laplace transformation theory. Numerical simulations show the effectiveness of the theoretical analyses.     

Experimental observation of direct current voltage-induced phase synchronization

The dynamics of two uncoupled distinct Chua circuits driven by a common direct current voltage is explored experimentally. It was found that, with increasing current intensity, the dominant frequencies of these two Chua circuits will first vary at different speeds, approach an identical value for a certain current intensity and then separate. Techniques such as synchronization index and phase difference distribution were employed to analyze the phase coherence between these two Chua circuits.