Control of Continuous Time Chaotic Systems With Unknown Dynamics and Limitation on State Measurement

2018 ◽  
Vol 14 (1) ◽  
Author(s):  
Hojjat Kaveh ◽  
Hassan Salarieh
Keyword(s):  
Chaotic Attractor ◽  
Chaos Control ◽  
Chaotic Systems ◽  
Control Method ◽  
Original System ◽  
Control Of Chaos ◽  
State Measurement ◽  
New Chaotic Attractor ◽  
Systematic Control ◽  
Takens Embedding

This paper has dedicated to study the control of chaos when the system dynamics is unknown and there are some limitations on measuring states. There are many chaotic systems with these features occurring in many biological, economical and mechanical systems. The usual chaos control methods do not have the ability to present a systematic control method for these kinds of systems. To fulfill these strict conditions, we have employed Takens embedding theorem which guarantees the preservation of topological characteristics of the chaotic attractor under an embedding named “Takens transformation.” Takens transformation just needs time series of one of the measurable states. This transformation reconstructs a new chaotic attractor which is topologically similar to the unknown original attractor. After reconstructing a new attractor its governing dynamics has been identified. The measurable state of the original system which is one of the states of the reconstructed system has been controlled by delayed feedback method. Then the controlled measurable state induced a stable response to all of the states of the original system.

Comparison of Times of Synchronization of Chaotic Burke-Shaw Attractor with Active Control and Integer and Optimum Fractional-Order Pecaro Carroll Method

2021 ◽  
Author(s):  
Ali Durdu ◽  
Yılmaz Uyaroğlu
Keyword(s):  
Active Control ◽  
Fractional Order ◽  
Chaotic Attractor ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Control Method ◽  
Initial Conditions ◽  
Data Communication ◽  
Experimental Results ◽  
Active Control Method

Abstract Many studies have been introduced in the literature showing that two identical chaotic systems can be synchronized with different initial conditions. Secure data communication applications have also been made using synchronization methods. In the study, synchronization times of two popular synchronization methods are compared, which is an important issue for communication. Among the synchronization methods, active control, integer, and fractional-order Pecaro Carroll (P-C) method was used to synchronize the Burke-Shaw chaotic attractor. The experimental results showed that the P-C method with optimum fractional-order is synchronized in 2.35 times shorter time than the active control method. This shows that the P-C method using fractional-order creates less delay in synchronization and is more convenient to use in secure communication applications.

PERIODIC RESPONSE TO EXTERNAL STIMULATION OF A CHAOTIC NEURAL NETWORK WITH DELAYED FEEDBACK

1999 ◽  
Vol 09 (04) ◽  
pp. 713-722 ◽  
Author(s):  
ALBAN PUI MAN TSUI ◽  
ANTONIA J. JONES
Keyword(s):  
Neural Network ◽  
Chaos Control ◽  
Control Method ◽  
Original System ◽  
Neural System ◽  
Delayed Feedback ◽  
Input Stimulus ◽  
Biologically Inspired ◽  
External Stimulation ◽  
Different Types

We construct a feedforward neural network so that when the outputs are fed back into the inputs and the system is iterated it behaves chaotically. We call this the "rest state". Suppose now that an input stimulus is added to one or more inputs. Following a biologically inspired model suggested by Freeman [1991], under these conditions we should want the behavior of the network to stabilize into an unstable periodic orbit of the original system. We call this the "retrieval behavior" since it is analogous to the act of recognition. Standard methods of chaos control, such as OGY for example, used to elicit the retrieval behavior would be inappropriate, since such methods involve calculations external to the system being controlled and can be considered unlikely in a biological neural network. Using a chaos control method originally suggested by Pyragas [1992] we show that retrieval behavior can occur as a result of delayed feedback and examine the variety of the responses that arise under different types of stimuli and under noise. This artificial neural system has a strong dynamical parallel to Freeman's observed biological phenomenon.

Combination of Improved OGY and Guiding Orbit Method for Chaos Control

2019 ◽  
Vol 23 (5) ◽  
pp. 847-855 ◽  
Author(s):  
Lingzhi Yi ◽  
Yue Liu ◽  
Wenxin Yu ◽  
◽  
◽  
...  
Keyword(s):  
Chaotic System ◽  
Chaos Control ◽  
Chaotic Systems ◽  
Control Method ◽  
Search Algorithm ◽  
Cuckoo Search ◽  
Cuckoo Search Algorithm ◽  
Convergence Speed ◽  
Orbit Method ◽  
Modified Method

Chaotic systems have gathered much attention. When the OGY method is applied to control a chaotic system, chaos can be contained and target signals can be traced with satisfactory accuracy. However, the traditional control method have a low convergence speed, which may hamper the performance of the whole system. To solve this problem, the cuckoo search algorithm is used to guide the orbits of chaotic systems. Moreover, the OGY method is improved so that a chaotic system can be stabilized for different target points. Finally, the effectiveness of the proposed method is verified through several typical chaotic systems. The simulation results indicate that the modified method has a faster convergence speed and yields better performance than the traditional OGY control method.

TIME DELAYED REPETITIVE LEARNING CONTROL FOR CHAOTIC SYSTEMS

2002 ◽  
Vol 12 (05) ◽  
pp. 1057-1065 ◽  
Author(s):  
YANXING SONG ◽  
XINGHUO YU ◽  
GUANRONG CHEN ◽  
JIAN-XIN XU ◽  
YU-PING TIAN
Keyword(s):  
Periodic Orbits ◽  
Adaptive Learning ◽  
Chaos Control ◽  
Chaotic Systems ◽  
Control Method ◽  
Learning Control ◽  
Control Technique ◽  
Unstable Periodic Orbits ◽  
Repetitive Learning ◽  
Control Principle

In this paper, a time-delayed chaos control method based on repetitive learning is proposed. A general repetitive learning control structure based on the invariant manifold of the chaotic system is given. The integration of the repetitive learning control principle and the time-delayed chaos control technique enables adaptive learning of appropriate control actions from learning cycles. In contrast to the conventional repetitive learning control, no exact knowledge (analytic representation) of the target unstable periodic orbits is needed, except for the time delay constant, which can be identified via either experiments or adaptive learning. The controller effectively stabilizes the states of the continuous-time chaos on desired unstable periodic orbits. Simulations on the Duffing and Lorenz chaotic systems are provided to verify the design and analysis.

A New Chaotic Attractor Around a Pre-Located Ring

2017 ◽  
Vol 27 (10) ◽  
pp. 1750152 ◽  
Author(s):  
Zhen Wang ◽  
Zhe Xu ◽  
Ezzedine Mliki ◽  
Akif Akgul ◽  
Viet-Thanh Pham ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Chaotic System ◽  
Chaotic Attractor ◽  
Chaotic Systems ◽  
Specific Property ◽  
Unique Property ◽  
Circuit Implementation ◽  
New Chaotic System ◽  
New Chaotic Attractor ◽  
New System

Designing chaotic systems with specific features is a very interesting topic in nonlinear dynamics. However most of the efforts in this area are about features in the structure of the equations, while there is less attention to features in the topology of strange attractors. In this paper, we introduce a new chaotic system with unique property. It has been designed in such a way that a specific property has been injected to it. This new system is analyzed carefully and its real circuit implementation is presented.

Coupled Feedback Control of Chaos in the Qi System

2011 ◽  
Vol 480-481 ◽  
pp. 1368-1372
Author(s):  
Jing Yue Wang ◽  
Hao Tian Wang
Keyword(s):  
Time Course ◽  
Chaotic Systems ◽  
Control Method ◽  
Complex Dynamics ◽  
Phase Portraits ◽  
Unstable Periodic Orbit ◽  
Control Of Chaos ◽  
Feedback Strategy ◽  
Regular Motion ◽  
Route To Chaos

The complex dynamics behavior of the four-dimensional Qi system is studied. The route to chaos of the system is studied by the time course diagram, phase portraits and Poincaré maps. We use a Coupled feedback strategy to control the chaotic motion towards regular motion. Numerical simulation shows the effectiveness and feasibility of the strategy to get rid of chaos by stabilizing the related unstable periodic orbit. This control method can be applied to other chaotic systems.

Fractional Dynamic Sliding Mode Control for uncertain chaotic systems Applied to a Chaotic Robot arm under dynamic load.

2020 ◽  
Vol 10 ◽  
Author(s):  
Sara Gholipour P ◽  
Sara Minagar ◽  
Javad Kazemitabar ◽  
Mobin Alizadeh
Keyword(s):  
Sliding Mode Control ◽  
Chaotic Systems ◽  
Control Method ◽  
Sliding Mode ◽  
Qualitative And Quantitative ◽  
Mode Control ◽  
Quantitative Characteristics ◽  
Dynamic Sliding Mode Control ◽  
Dynamic Sliding Mode ◽  
Qualitative And Quantitative Characteristics

Background: A novel type of control strategy is presented for control of chaotic systems particularly a chaotic robot in joint and workspace which is the result of applying fractional calculus to dynamic sliding mode control. Objectives: To guarantee the sliding mode condition, control law is introduced based on the Lyapunov stability theory. Methods: A control scheme is proposed for reducing the chattering problem in finite time tracking and robust in presence of system matched disturbances. Conclusion: Also, all of chaotic robot's qualitative and quantitative characteristics have been investigated. Numerical simulations indicate viability of our control method. Results: Qualitative and quantitative characteristics of the chaotic robot are all proven to be viable thru simulations.

scholarly journals Universal Projective Synchronization of Two Different Hyperchaotic Systems with Unknown Parameters

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Baojie Zhang ◽  
Hongxing Li
Keyword(s):  
Adaptive Control ◽  
Chaotic Systems ◽  
Control Method ◽  
Scaling Function ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Reference Systems ◽  
Unknown Parameters ◽  
Hyperchaotic Systems ◽  
Function Matrix

Universal projective synchronization (UPS) of two chaotic systems is defined. Based on the Lyapunov stability theory, an adaptive control method is derived such that UPS of two different hyperchaotic systems with unknown parameters is realized, which is up to a scaling function matrix and three kinds of reference systems, respectively. Numerical simulations are used to verify the effectiveness of the scheme.

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