scholarly journals The Exponential Stabilization of a Class of n-D Chaotic Systems via the Exact Solution Method

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Runzi Luo ◽  
Jiaojiao Fu ◽  
Haipeng Su
Keyword(s):  
Numerical Simulation ◽  
Exact Solution ◽  
Theoretical Analysis ◽  
Chaotic System ◽  
Unknown Parameter ◽  
Chaotic Systems ◽  
Solution Method ◽  
Exponential Stabilization ◽  
Control Approach

This paper treats the exponential stabilization of a class of n-D chaotic systems. A new control approach which is called the exact solution method is presented. The most important feature of this method is that the solution of the system under consideration can be carefully designed to converge exponentially to the origin. Based on this method, the exponential stabilization of a class of n-D chaotic systems and its application in controlling chaotic system with unknown parameter are presented. The Genesio-Tesi system is taken to give the numerical simulation which is completely consistent with the theoretical analysis presented in this paper.

A New Dynamic System Analysis

2013 ◽  
Vol 392 ◽  
pp. 222-226
Author(s):  
Bao Liang Mi ◽  
Guo Zeng Wu
Keyword(s):  
Numerical Simulation ◽  
Theoretical Analysis ◽  
Dynamic System ◽  
Bifurcation Diagram ◽  
Chaotic System ◽  
System Analysis ◽  
Electronic Circuit ◽  
Circuit Implementation ◽  
Dynamical Properties ◽  
Electronic Circuit Implementation

A new four-dimensional chaotic system is presented in this paper. Some basic dynamical Properties of this chaotic system are investigated by means of Poincaré mapping, Lyapunov exponents and bifurcation diagram. The dynamical behaviours of this system are proved not only by performing numerical simulation and brief theoretical analysis but also by conducting an electronic circuit implementation.

Bursting, Dynamics, and Circuit Implementation of a New Fractional-Order Chaotic System With Coexisting Hidden Attractors

2019 ◽  
Vol 14 (7) ◽  
Author(s):  
Meng Jiao Wang ◽  
Xiao Han Liao ◽  
Yong Deng ◽  
Zhi Jun Li ◽  
Yi Ceng Zeng ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Fractional Order ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Equilibrium Points ◽  
Neuroendocrine Cells ◽  
Order System ◽  
Hidden Attractors ◽  
Main Mode ◽  
Circuit Realization

Systems with hidden attractors have been the hot research topic of recent years because of their striking features. Fractional-order systems with hidden attractors are newly introduced and barely investigated. In this paper, a new 4D fractional-order chaotic system with hidden attractors is proposed. The abundant and complex hidden dynamical behaviors are studied by nonlinear theory, numerical simulation, and circuit realization. As the main mode of electrical behavior in many neuroendocrine cells, bursting oscillations (BOs) exist in this system. This complicated phenomenon is seldom found in the chaotic systems, especially in the fractional-order chaotic systems without equilibrium points. With the view of practical application, the spectral entropy (SE) algorithm is chosen to estimate the complexity of this fractional-order system for selecting more appropriate parameters. Interestingly, there is a state variable correlated with offset boosting that can adjust the amplitude of the variable conveniently. In addition, the circuit of this fractional-order chaotic system is designed and verified by analog as well as hardware circuit. All the results are very consistent with those of numerical simulation.

Robust Control and Synchronization of Chaotic Systems with Actuator Constraints

2015 ◽  
pp. 1-43 ◽  
Author(s):  
Kouamana Bousson ◽  
Carlos Velosa
Keyword(s):  
Robust Control ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Linear Part ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Aeroelastic System ◽  
Control Approach ◽  
Nonlinear Part ◽  
Actuator Constraints

This chapter proposes a robust control approach for the class of chaotic systems subject to magnitude and rate actuator constraints. The approach consists of decomposing the chaotic system into a linear part plus a nonlinear part to form an augmented system comprising the system itself and the integral of the output error. The resulting system is posteriorly seen as a linear system plus a bounded disturbance, and two robust controllers are applied: first, a controller based on a generalization of the Lyapunov function, then a Linear-Quadratic Regulator (LQR) with a prescribed degree of stability. Numerical simulations are performed to validate the approach applying it to the Lorenz chaotic system and to a chaotic aeroelastic system, and parameter uncertainties are also considered to prove its robustness. The results confirm the effectiveness of the approach, and the constraints are guaranteed as opposed to other control techniques which do not consider any kind of constraints.

Anti-Synchronization for a Modified Chen-Qi-Like Chaotic System

2012 ◽  
Vol 220-223 ◽  
pp. 2113-2116
Author(s):  
Su Hai Huang
Keyword(s):  
Numerical Simulation ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Stability Theorem ◽  
Control Law ◽  
Lyapunov Stability Theorem ◽  
Unknown Parameters ◽  
Dynamical Characteristics ◽  
Control Scheme ◽  
Adaptive Control Scheme

A modified Chen-Qi-like chaotic system is presented. Some basic dynamical characteristics of this system are studied by calculating the Lyapunov exponent and phase figure. Based on the Lyapunov stability theorem, adaptive control scheme and parameters update law are presented for the anti-synchronization of new chaotic systems with fully unknown parameters. Finally, the numerical simulation verify that the control law and parameter changing are correct.

Constructing Chaotic Systems from a Class of Switching Systems

2018 ◽  
Vol 28 (02) ◽  
pp. 1850032 ◽  
Author(s):  
Yuping Zhang ◽  
Xinzhi Liu ◽  
Huaiyue Zhang ◽  
Chunhua Jia
Keyword(s):  
Numerical Simulation ◽  
Theoretical Analysis ◽  
Continuous Time ◽  
Chaotic Systems ◽  
Switching Systems ◽  
Heteroclinic Loop ◽  
Time Switching ◽  
Loop Design ◽  
Implementation Scheme ◽  
Shilnikov Criterion

This paper aims to develop an approach for constructing chaotic systems from a class of linear continuous-time switching systems. First, the Shilnikov criterion is analyzed and extended to the switching systems. Then some kinds of “swing planes” are provided via a heteroclinic loop design, which act as switching planes to chaotify the systems. Furthermore, a numerical example is presented to validate the proposed principle and implementation scheme. The theoretical analysis and numerical simulation have demonstrated the feasibility and effectiveness of the developed techniques.

Generating a Double-Scroll Attractor by Connecting a Pair of Mutual Mirror-Image Attractors via Planar Switching Control

2017 ◽  
Vol 27 (13) ◽  
pp. 1750197 ◽  
Author(s):  
Changchun Sun ◽  
Zhongtang Chen ◽  
Qicheng Xu
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Three Dimensional ◽  
Switching Control ◽  
Mirror Image ◽  
Image System ◽  
Sign Function ◽  
Control Approach ◽  
Switching Law ◽  
Dynamical Behaviors

An original three-dimensional (3D) smooth continuous chaotic system and its mirror-image system with eight common parameters are constructed and a pair of symmetric chaotic attractors can be generated simultaneously. Basic dynamical behaviors of two 3D chaotic systems are investigated respectively. A double-scroll chaotic attractor by connecting the pair of mutual mirror-image attractors is generated via a novel planar switching control approach. Chaos can also be controlled to a fixed point, a periodic orbit and a divergent orbit respectively by switching between two chaotic systems. Finally, an equivalent 3D chaotic system by combining two 3D chaotic systems with a switching law is designed by utilizing a sign function. Two circuit diagrams for realizing the double-scroll attractor are depicted by employing an improved module-based design approach.

scholarly journals Controlling Chaotic Systems via Time-delayed Control

2021 ◽  
Vol 15 ◽  
pp. 44-49
Author(s):  
Ramy Farid ◽  
Abdul-Azim Ibrahim ◽  
Belal Abou-Zalam
Keyword(s):  
Numerical Simulation ◽  
Theoretical Analysis ◽  
Chaotic Systems ◽  
Equilibrium Points ◽  
Unstable Equilibrium ◽  
Chaotic Attractors ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Integral Time ◽  
Lyapunov Stabilization

Based on Lyapunov stabilization theory, this paper proposes a proportional plus integral time-delayed controller to stabilize unstable equilibrium points (UPOs) embedded in chaotic attractors. The criterion is successfully applied to the classic Chua's circuit. Theoretical analysis and numerical simulation show the effectiveness of this controller.

Multiscroll Hyperchaotic System with Hidden Attractors and Its Circuit Implementation

2019 ◽  
Vol 29 (09) ◽  
pp. 1950117 ◽  
Author(s):  
Xin Zhang ◽  
Chunhua Wang
Keyword(s):  
Numerical Simulation ◽  
Adaptive Control ◽  
Theoretical Analysis ◽  
Chaotic System ◽  
Control Method ◽  
Hyperchaotic System ◽  
Circuit Implementation ◽  
Hidden Attractors ◽  
System A ◽  
Simulation Results

Based on the study on Jerk chaotic system, a multiscroll hyperchaotic system with hidden attractors is proposed in this paper, which has infinite number of equilibriums. The chaotic system can generate [Formula: see text] scroll hyperchaotic hidden attractors. The dynamic characteristics of the multiscroll hyperchaotic system with hidden attractors are analyzed by means of dynamic analysis methods such as Lyapunov exponents and bifurcation diagram. In addition, we have studied the synchronization of the system by applying an adaptive control method. The hardware experiment of the proposed multiscroll hyperchaotic system with hidden attractors is carried out using discrete components. The hardware experimental results are consistent with the numerical simulation results of MATLAB and the theoretical analysis results.

scholarly journals Dynamic Analysis and Robust Control of a Chaotic System with Hidden Attractor

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Huaigu Tian ◽  
Zhen Wang ◽  
Peijun Zhang ◽  
Mingshu Chen ◽  
Yang Wang
Keyword(s):  
Numerical Simulation ◽  
Robust Control ◽  
Theoretical Analysis ◽  
Chaotic System ◽  
Finite Time ◽  
Original System ◽  
Slave System ◽  
Hidden Attractor ◽  
Time Stability ◽  
Finite Time Stability

In this paper, a 3D jerk chaotic system with hidden attractor was explored, and the dissipativity, equilibrium, and stability of this system were investigated. The attractor types, Lyapunov exponents, and Poincare section of the system under different parameters were analyzed. Additionally, a circuit was carried out, and a good similarity between the circuit experimental results and the theoretical analysis testifies the feasibility and practicality of the original system. Furthermore, a robust feedback controller was designed based on the finite-time stability theory, which guarantees the synchronization of 3D jerk master-slave system in finite time and asymptotically converges to the origin. Finally, we also give verification for the discussion in this paper by numerical simulation.

FURTHER RESULTS ON FUNCTIONAL PROJECTIVE SYNCHRONIZATION OF GENESIO–TESI CHAOTIC SYSTEM

2009 ◽  
Vol 23 (15) ◽  
pp. 1889-1895 ◽  
Author(s):  
JU H. PARK
Keyword(s):  
Numerical Simulation ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Feedback Controller ◽  
Projective Synchronization ◽  
Linear Dynamic ◽  
Synchronization Problem ◽  
Control Scheme ◽  
Static Feedback ◽  
Nonlinear Static

This letter considers the functional projective synchronization problem for Genesio–Tesi chaotic systems. Based on our earlier work, a new control scheme, which consists of a linear dynamic controller and a nonlinear static feedback controller, is applied to achieve the synchronization. A numerical simulation is presented to show the usefulness of the proposed control scheme.

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