Learning Control of Time-Delay Chaotic Systems and its Applications

1998 ◽  
Vol 08 (12) ◽  
pp. 2457-2465 ◽  
Author(s):  
Keiji Konishi ◽  
Hideki Kokame
Keyword(s):  
Control System ◽  
Time Delay ◽  
Chaotic System ◽  
Numerical Experiments ◽  
Chaotic Systems ◽  
Learning Control ◽  
Uncertain Information ◽  
Stable Orbit ◽  
One Dimensional ◽  
Theoretical Results

The present paper proposes a learning control system that automatically stabilizes one-dimensional time-delayed chaotic systems. We give a systematic procedure to design the control system using a few pieces of uncertain information on the chaotic system. Furthermore, this control system can be applied to a technique that moves a stable orbit of nonchaotic systems to coexistent unstable points and stabilizes the moving orbit onto these unstable points. To check the theoretical results, we demonstrate some numerical experiments.

scholarly journals FPGA Realization and Lyapunov–Krasovskii Analysis for a Master-Slave Synchronization Scheme Involving Chaotic Systems and Time-Delay Neural Networks

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
J. Perez-Padron ◽  
C. Posadas-Castillo ◽  
J. Paz-Perez ◽  
E. Zambrano-Serrano ◽  
M. A. Platas-Garza
Keyword(s):  
Time Delay ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Tracking Error ◽  
Control Law ◽  
Trajectory Tracking Control ◽  
Field Programmable ◽  
Different Chaotic Systems ◽  
Synchronization Scheme ◽  
Theoretical Results

In this paper, the trajectory tracking control and the field programmable gate array (FPGA) implementation between a recurrent neural network with time delay and a chaotic system are presented. The tracking error is globally asymptotically stabilized by means of a control law generated from the Lyapunov–Krasovskii and Lur’e theory. The applicability of the approach is illustrated by considering two different chaotic systems: Liu chaotic system and Genesio–Tesi chaotic system. The numerical results have shown the effectiveness of obtained theoretical results. Finally, the theoretical results are implemented on an FPGA, confirming the feasibility of the synchronization scheme and showing that it is hardware realizable.

scholarly journals Hybrid Passivity Based and Fuzzy Type-2 Controller for Chaotic and Hyper-Chaotic Systems

2017 ◽  
Vol 11 (2) ◽  
pp. 96-103 ◽  
Author(s):  
Fernando Serrano ◽  
Josep M. Rossell
Keyword(s):  
Lyapunov Exponents ◽  
Chaotic System ◽  
Control Strategy ◽  
Chaotic Systems ◽  
Control Law ◽  
Four Dimensions ◽  
Design Requirements ◽  
The Stability ◽  
Theoretical Results

AbstractIn this paper a hybrid passivity based and fuzzy type-2 controller for chaotic and hyper-chaotic systems is presented. The proposed control strategy is an appropriate choice to be implemented for the stabilization of chaotic and hyper-chaotic systems due to the energy considerations of the passivity based controller and the flexibility and capability of the fuzzy type-2 controller to deal with uncertainties. As it is known, chaotic systems are those kinds of systems in which one of their Lyapunov exponents is real positive, and hyper-chaotic systems are those kinds of systems in which more than one Lyapunov exponents are real positive. In this article one chaotic Lorentz attractor and one four dimensions hyper-chaotic system are considered to be stabilized with the proposed control strategy. It is proved that both systems are stabilized by the passivity based and fuzzy type-2 controller, in which a control law is designed according to the energy considerations selecting an appropriate storage function to meet the passivity conditions. The fuzzy type-2 controller part is designed in order to behave as a state feedback controller, exploiting the flexibility and the capability to deal with uncertainties. This work begins with the stability analysis of the chaotic Lorentz attractor and a four dimensions hyper-chaotic system. The rest of the paper deals with the design of the proposed control strategy for both systems in order to design an appropriate controller that meets the design requirements. Finally, numerical simulations are done to corroborate the obtained theoretical results.

scholarly journals Control of Chaos Using Sampled-Data Feedback Control

1998 ◽  
Vol 08 (12) ◽  
pp. 2433-2438 ◽  
Author(s):  
Tao Yang
Keyword(s):  
Feedback Control ◽  
Asymptotic Stability ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Sampling Rate ◽  
Control Input ◽  
Sampled Data ◽  
Control Of Chaos ◽  
Data Feedback ◽  
Theoretical Results

In this paper we present a theory for control of chaotic systems using sampled data. The output of the chaotic system is sampled at a given sampling rate and the sampled output is used by a feedback subsystem to construct a control signal, which is held constant by a holding subsystem. Hence, during each control iteration, the control input remains unchanged. Theoretical results on the asymptotic stability of the resulting controlled chaotic systems are presented. Numerical experimental results via Chua's circuit are used to verify the theoretical results.

scholarly journals Consensus Learning Control for Leader-Following Nonlinear Multiagent Systems with Control Delay

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Xiongfeng Deng ◽  
Xiuxia Sun ◽  
Shuguang Liu
Keyword(s):  
Time Delay ◽  
Multiagent Systems ◽  
Iterative Learning Control ◽  
Learning Control ◽  
Control Delay ◽  
Consensus Tracking ◽  
Control Scheme ◽  
Communication Topology ◽  
Leader Following ◽  
Theoretical Results

In this paper, the consensus tracking problem of leader-following nonlinear control time-delay multiagent systems with directed communication topology is addressed. An improved high-order iterative learning control scheme with time-delay is proposed, where the local information between agents is considered. The uniformly global Lipschitz condition is applied to deal with the nonlinear dynamics. Then, a sufficient condition is driven, which guarantees that all the following agents track the trajectory of leader. Also, the convergence of proposed control protocol is analyzed by the norm theory. Finally, two cases are provided to illustrate the validity of theoretical results.

Chaos Suppression via Integrative Time Delay Control

2020 ◽  
Vol 30 (14) ◽  
pp. 2050208
Author(s):  
Ayman A. Arafa ◽  
Yong Xu ◽  
Gamal M. Mahmoud
Keyword(s):  
Time Delay ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Time Interval ◽  
General Strategy ◽  
Normal Form Theory ◽  
Chaos Suppression ◽  
Form Theory ◽  
The Stability ◽  
Time Delayed Feedback

A general strategy for suppressing chaos in chaotic Burke–Shaw system using integrative time delay (ITD) control is proposed, as an example. The idea of ITD is that the feedback is integrated over a time interval. Physically, the chaotic system responds to the average information it receives from the feedback. The main feature of integrative is that the stability of the chaotic system occurs over a wider range of the space parameters. Controlling chaotic systems with ITD has not been discussed before as far as we know. Stability and the existence of Hopf bifurcation are studied which demonstrate that the switch stability occurs at critical values of the time delay. Employing the normal form theory and center manifold argument, an explicit formula is derived to determine the stability and the direction of the bifurcating periodic solutions. Numerically, the bifurcation diagram and the eigenvalues of the corresponding characteristic equations are computed to supply a clear interpretation for suppressing chaos via ITD. Furthermore, ITD method is compared with the time delayed feedback (TDF) control numerically. This comparison shows that the stability area with ITD is larger than TDF which demonstrates the feasibility and effectiveness of the ITD. Other examples of chaotic systems can be similarly investigated.

Lag-generalized synchronization of time-delay chaotic systems with stochastic perturbation

2016 ◽  
Vol 30 (01) ◽  
pp. 1550263 ◽  
Author(s):  
Shuo Zhang ◽  
Yongguang Yu ◽  
Guoguang Wen ◽  
Ahmed Rahmani
Keyword(s):  
Time Delay ◽  
Unknown Parameter ◽  
Chaotic Systems ◽  
Stochastic Perturbation ◽  
Generalized Synchronization ◽  
Unknown Parameters ◽  
Control Laws ◽  
Numerical Examples ◽  
Error System ◽  
Theoretical Results

The lag-generalized synchronization of coupled time-delay chaotic systems with unknown parameters and stochastic perturbation is investigated. Based on the LaSalle-type invariance principle of stochastic differential equation, the synchronization is realized by analyzing stochastic stability of the error system. In order to achieve the synchronization, the unknown parameter update laws and the control laws are proposed. At last, two numerical examples are presented to show the effectiveness of the obtained theoretical results.

Analysis of Geometrically Consistent Schemes with Finite Range Interaction

2017 ◽  
Vol 22 (5) ◽  
pp. 1333-1361
Author(s):  
Hongliang Li ◽  
Pingbing Ming
Keyword(s):  
Error Estimate ◽  
Numerical Experiments ◽  
Optimal Error Estimate ◽  
Finite Range ◽  
Dimensional Problem ◽  
Optimal Error ◽  
Range Interaction ◽  
One Dimensional ◽  
Sharp Stability ◽  
Theoretical Results

AbstractWe analyze the geometrically consistent schemes proposed by E. Lu and Yang [6] for one-dimensional problem with finite range interaction. The existence of the reconstruction coefficients is proved, and optimal error estimate is derived under sharp stability condition. Numerical experiments are performed to confirm the theoretical results.

ANALYTICAL CONDITIONS FOR AMPLITUDE DEATH INDUCED BY CONJUGATE VARIABLE COUPLINGS

2011 ◽  
Vol 21 (01) ◽  
pp. 225-235 ◽  
Author(s):  
XIAOMING ZHANG ◽  
YINGCHUN WU ◽  
JIANHUA PENG
Keyword(s):  
Numerical Simulations ◽  
Chaotic System ◽  
Arbitrary Number ◽  
Chaotic Systems ◽  
Amplitude Death ◽  
Chaotic Oscillators ◽  
Conjugate Variable ◽  
Global Coupling ◽  
Theoretical Results

We construct local and global conjugate variable coupled chaotic systems with an arbitrary number of identical chaotic oscillators. Amplitude death phenomena are found in these two kinds of systems. General methods are proposed to theoretically analyze conditions for amplitude death under local and global conditions, respectively. Taking the Rössler chaotic system as the oscillator unit, we apply these methods to determine the analytical conditions for amplitude death. And the transition relations between local and global coupling induced amplitude deaths are also given. All theoretical results are well confirmed by numerical simulations.

scholarly journals Chaos Control and Synchronization via Switched Output Control Strategy

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Runzi Luo ◽  
Haipeng Su ◽  
Yanhui Zeng
Keyword(s):  
Chaotic System ◽  
Control Strategy ◽  
Chaos Control ◽  
Chaotic Systems ◽  
State Variables ◽  
Output Control ◽  
Lorenz Chaotic System ◽  
Control And Synchronization ◽  
Theoretical Results

This paper investigates the control and synchronization of a class of chaotic systems with switched output which is assumed to be switched between the first and the second state variables of chaotic system. Some novel and yet simple criteria for the control and synchronization of a class of chaotic systems are proposed via the switched output. The generalized Lorenz chaotic system is taken as an example to show the feasibility and efficiency of theoretical results.

scholarly journals On an Impulsive Food Web System with Mutual Interference and Distributed Time Delay

2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Zhen Wang ◽  
Liwei Liu ◽  
Guangwang Su ◽  
Yuanfu Shao
Keyword(s):  
Time Delay ◽  
Food Web ◽  
Numerical Experiments ◽  
Perturbation Technique ◽  
Dynamical Behavior ◽  
Chaotic Oscillation ◽  
Mutual Interference ◽  
Web System ◽  
Distributed Time Delay ◽  
Theoretical Results

In this paper, we present a predator-prey system with mutual interference and distributed time delay and study its dynamical behavior. Based on the existence and universality of mutual interference among species, it is necessary to further study an impulsive food web system. By using stability theory, slight perturbation technique, and comparison theorem, we obtain some theoretical results of the system, such as boundedness and permanence. Moreover, numerical experiments are used to verify the theoretical results and to explore the dynamical behavior of the system, which exhibits rich dynamical behavior such as chaotic oscillation, periodic oscillation, symmetry-breaking bifurcations, chaotic crises, and period bifurcation. Finally, we give some practical guidelines for biological systems based on the theoretical results and numerical experiments of the system.

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