A Memristor-Based Lorenz Circuit and Its Stabilization via Variable-Time Impulsive Control

2017 ◽  
Vol 27 (03) ◽  
pp. 1750031 ◽  
Author(s):  
Po Wu ◽  
Chuandong Li ◽  
Xing He ◽  
Tingwen Huang
Keyword(s):  
Chaotic System ◽  
Impulsive Control ◽  
Chaotic Behavior ◽  
Fixed Time ◽  
Impulsive System ◽  
Variable Time ◽  
Memristive System ◽  
The Stability ◽  
Memristor Emulator ◽  
Impulsive Stabilization

In this paper, an off-the-shelf memristor emulator of the quadratic memristor is developed and applied to a Lorenz circuit. The impulsive stabilization of the chaotic system by variable moments of impulses is investigated. By B-equivalence method, the considered variable-time impulsive system can be reduced to the fixed-time impulsive one. The simulations of the chaotic behavior verify the effectiveness of the emulator-based memristive system. The stability simulations support the validity of the method.

Impulsive Control and Synchronization of Memristor-Based Chaotic Circuits

2014 ◽  
Vol 24 (12) ◽  
pp. 1450162 ◽  
Author(s):  
Shiju Yang ◽  
Chuandong Li ◽  
Tingwen Huang
Keyword(s):  
Chaotic System ◽  
Impulsive Control ◽  
Chaotic Behavior ◽  
Memory Function ◽  
Sufficient Conditions ◽  
Impulsive System ◽  
Circuit Element ◽  
Chaotic Circuits ◽  
Control And Synchronization ◽  
Passive Circuit

The memristor is a novel nonlinear passive circuit element which has the memory function, and the circuits based on the memristors might exhibit chaotic behavior. In this paper, we revisit a memristor-based chaotic circuit, and then investigate its stabilization and synchronization via impulsive control. By impulsive system theory, some sufficient conditions for the stabilization and synchronization of the memristor-based chaotic system are established. Moreover, an estimation of the upper bound of the impulse interval is proposed under the condition that the parameters of the chaotic system and the impulsive control law are well defined. To show the effectiveness of the theoretical results, numerical simulations are also presented.

Nonlinear Dynamic Analysis of a Simplest Fractional-Order Delayed Memristive Chaotic System

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
Wei Hu ◽  
Dawei Ding ◽  
Nian Wang
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Chaotic System ◽  
Chaotic Behavior ◽  
Nonlinear Dynamic Analysis ◽  
Period Doubling ◽  
Transversality Condition ◽  
Memristive System ◽  
Route To Chaos ◽  
The Stability

A simplest fractional-order delayed memristive chaotic system is investigated in order to analyze the nonlinear dynamics of the system. The stability and bifurcation behaviors of this system are initially investigated, where time delay is selected as the bifurcation parameter. Some explicit conditions for describing the stability interval and the transversality condition of the emergence for Hopf bifurcation are derived. The period doubling route to chaos behaviors of such a system is discussed by using a bifurcation diagram, a phase diagram, a time-domain diagram, and the largest Lyapunov exponents (LLEs) diagram. Specifically, we study the influence of time delay on the chaotic behavior, and find that when time delay increases, the transitions from one cycle to two cycles, two cycles to four cycles, and four cycles to chaos are observed in this system model. Corresponding critical values of time delay are determined, showing the lowest orders for chaos in the fractional-order delayed memristive system. Finally, numerical simulations are provided to verify the correctness of theoretical analysis using the modified Adams–Bashforth–Moulton method.

scholarly journals Time-Delayed Impulsive Control of Chaotic System Based on T-S Fuzzy Model

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Cheng Hu ◽  
Haijun Jiang
Keyword(s):  
Feedback Control ◽  
Chaotic System ◽  
Impulsive Control ◽  
Fuzzy Model ◽  
Delayed Feedback Control ◽  
Control Technique ◽  
The Stability ◽  
Control And Synchronization ◽  
Time Delayed Feedback ◽  
Delayed Impulsive Control

This paper is concerned with the time-delayed impulsive control and synchronization of general chaotic system based on T-S fuzzy model. By utilizing impulsive control theory, time-delayed feedback control technique, and T-S fuzzy model, some useful and new conditions are derived to guarantee the stability and synchronization of the addressed chaotic system. Finally, some numerical simulations are given to illustrate the effectiveness of the derived results.

IMPULSIVE CONTROL FOR T–S FUZZY SYSTEM AND ITS APPLICATION TO CHAOTIC SYSTEMS

2006 ◽  
Vol 16 (08) ◽  
pp. 2417-2423 ◽  
Author(s):  
YAN-WU WANG ◽  
ZHI-HONG GUAN ◽  
HUA O. WANG ◽  
JIANG-WEN XIAO
Keyword(s):  
Chaotic System ◽  
Fuzzy System ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Control Structure ◽  
Impulsive Control ◽  
Fuzzy Model ◽  
Chua's Circuit ◽  
Control Scheme ◽  
The Stability

An impulsive T–S fuzzy model is presented in this paper. The stability of impulsive controlled T–S fuzzy system has been analyzed theoretically. The proposed impulsive control scheme seems to have a simple control structure and may need less control energy than the normal continuous ones for the stabilization of T–S fuzzy system. Some typical chaotic systems, such as Chua's circuit, Lorenz system and Chen's chaotic system, are considered as illustrations to demonstrate the effectiveness of the proposed control scheme.

scholarly journals Distributed Impulsive Consensus of the Multiagent System without Velocity Measurement

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Zhi-Wei Liu ◽  
Hong Zhou ◽  
Zhi-Hong Guan ◽  
Wen-Shan Hu ◽  
Li Ding ◽  
...  
Keyword(s):  
Velocity Measurement ◽  
Multiagent System ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Laplacian Matrix ◽  
Impulsive System ◽  
Consensus Algorithm ◽  
Communication Graph ◽  
The Stability ◽  
Necessary And Sufficient

This paper deals with the distributed consensus of the multiagent system. In particular, we consider the case where the velocity (second state) is unmeasurable and the communication among agents occurs at sampling instants. Based on the impulsive control theory, we propose an impulsive consensus algorithm that extends some of our previous work to account for the lack of velocity measurement. By using the stability theory of the impulsive system, some necessary and sufficient conditions are obtained to ensure the consensus of the controlled multiagent system. It is shown that the control gains, the sampled period and the eigenvalues of Laplacian matrix of communication graph play key roles in achieving consensus. Finally, a numerical simulation is provided to illustrate the effectiveness of the proposed algorithm.

IMPULSIVE CONTROL OF CHAOTIC SYSTEM

2002 ◽  
Vol 12 (05) ◽  
pp. 1181-1190 ◽  
Author(s):  
XINZHI LIU ◽  
KOK LAY TEO
Keyword(s):  
Feedback Control ◽  
Control Problem ◽  
Equilibrium Point ◽  
Chaotic System ◽  
Lyapunov Functions ◽  
Lorenz System ◽  
Impulsive Control ◽  
The Lorenz System ◽  
Impulsive Stabilization

This paper studies an impulsive control problem. By utilizing the method of Lyapunov functions, a set of impulsive stabilization criteria are established. These results are then applied to the Lorenz system. It is shown that by using impulsive feedback control, all the solutions of the Lorenz system will converge to an equilibrium point.

scholarly journals Finite-Time Lyapunov Functions and Impulsive Control Design

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Huijuan Li ◽  
Qingxia Ma
Keyword(s):  
Finite Time ◽  
Lyapunov Functions ◽  
Lorenz System ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Impulsive System ◽  
Impulsive Systems ◽  
Lyapunov Theorem ◽  
The Lorenz System ◽  
The Stability

In this paper, we introduce finite-time Lyapunov functions for impulsive systems. The relaxed sufficient conditions for asymptotic stability of an equilibrium of an impulsive system are given via finite-time Lyapunov functions. A converse finite-time Lyapunov theorem for controlling the impulsive system is proposed. Three examples are presented to show how to analyze the stability of an equilibrium of the considered impulsive system via finite-time Lyapunov functions. Furthermore, according to the results, we design an impulsive controller for a chaotic system modified from the Lorenz system.

The Tangled Tale of Phase Space

2018 ◽  
Author(s):  
David D. Nolte
Keyword(s):  
Phase Space ◽  
Chaotic Behavior ◽  
Three Body Problem ◽  
Henri Poincaré ◽  
History Of ◽  
The Stability ◽  
Three Body ◽  
Space Phase ◽  
Central Paradigm ◽  
System Phase

This chapter presents the history of the development of the concept of phase space. Phase space is the central visualization tool used today to study complex systems. The chapter describes the origins of phase space with the work of Joseph Liouville and Carl Jacobi that was later refined by Ludwig Boltzmann and Rudolf Clausius in their attempts to define and explain the subtle concept of entropy. The turning point in the history of phase space was when Henri Poincaré used phase space to solve the three-body problem, uncovering chaotic behavior in his quest to answer questions on the stability of the solar system. Phase space was established as the central paradigm of statistical mechanics by JW Gibbs and Paul Ehrenfest.

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