Stabilization of a Four-Dimensional Chaotic System with No Equilibria via a Novel Precise Constant-Control Approach

2021 ◽  
Author(s):  
Changchun Sun ◽  
Qicheng Xu
Keyword(s):  
Chaotic System ◽  
Control Approach ◽  
Constant Control ◽  
Precise Constant

CHAOTIFYING FUZZY HYPERBOLIC MODEL USING ADAPTIVE INVERSE OPTIMAL CONTROL APPROACH

2004 ◽  
Vol 14 (10) ◽  
pp. 3505-3517 ◽  
Author(s):  
HUAGUANG ZHANG ◽  
ZHILIANG WANG ◽  
DERONG LIU
Keyword(s):  
Optimal Control ◽  
Chaotic System ◽  
Parameter Tuning ◽  
Hyperbolic Model ◽  
Inverse Optimal Control ◽  
Control Approach ◽  
Adaptive Parameter ◽  
System A ◽  
Tuning Methods ◽  
Optimal Control Approach

In this paper, the problem of chaotifying the continuous-time fuzzy hyperbolic model (FHM) is studied. By tracking the dynamics of a chaotic system, a controller based on inverse optimal control and adaptive parameter tuning methods is designed to chaotify the FHM. Simulation results show that for any initial value the FHM can track a chaotic system asymptotically.

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.

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.

CONTROL OF CHUA'S CIRCUIT

1993 ◽  
Vol 03 (01) ◽  
pp. 173-194 ◽  
Author(s):  
TOM T. HARTLEY ◽  
FARAMARZ MOSSAYEBI
Keyword(s):  
Control Theory ◽  
State Space ◽  
Chaotic System ◽  
Harmonic Balance ◽  
Period Doubling ◽  
Chua’S Circuit ◽  
Input Output ◽  
Chua's Circuit ◽  
Control Approach ◽  
Balance Approach

This paper considers the control of a polynomial variant of the original Chua's circuit. Both state space techniques and input-output techniques are presented. It is shown that standard control theory approaches can easily accommodate a chaotic system. Furthermore, it is shown that a harmonic balance approach could predict the period doubling phenomenon and onset of the double scroll chaos, as well as providing a control approach.

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.

Controlling the Fractional-Order Chaotic System Based on Inverse Optimal Control Approach

2011 ◽  
Vol 474-476 ◽  
pp. 108-113
Author(s):  
Xin Gao
Keyword(s):  
Optimal Control ◽  
Fractional Order ◽  
Chaotic System ◽  
State Feedback ◽  
Fractional Order System ◽  
Order System ◽  
Inverse Optimal Control ◽  
Control Approach ◽  
Linear State ◽  
Optimal Control Approach

In this paper, we numerically investigate the chaotic behaviors of a fractional-order system. We find that chaotic behaviors exist in the fractional-order system with an order being less than 3. The lowest order we find to have chaos is 2.4 in such system. In addition, we numerically simulate the continuances of the chaotic behaviors in the fractional-order system with orders ranging from 2.7 to 3. Finally, a simple, but effective, linear state feedback controller is proposed for controlling the fractional-order chaotic system based on an inverse optimal control approach. Numerical simulations show the effectiveness and feasibility of the proposed controller.

Chaotic system synchronization with an unknown master model using a hybrid HOD active control approach

2009 ◽  
Vol 42 (3) ◽  
pp. 1900-1913 ◽  
Author(s):  
Shengzhi Du ◽  
Barend J. van Wyk ◽  
Guoyuan Qi ◽  
Chunling Tu
Keyword(s):  
Active Control ◽  
Chaotic System ◽  
Control Approach ◽  
System Synchronization ◽  
Master Model

scholarly journals Synchronization of an Uncertain Fractional-Order Chaotic System via Backstepping Sliding Mode Control

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Zhen Wang
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Chaotic System ◽  
Sliding Mode ◽  
Control Approach ◽  
Mode Control ◽  
System A ◽  
Control Scheme ◽  
Modeling Uncertainties ◽  
Backstepping Sliding Mode Control

Backstepping control approach combined with sliding mode control (SMC) technique is utilized to realize synchronization of uncertain fractional-order strict-feedback chaotic system. A backstepping SMC method is presented to compensate the uncertainty which occurs in the slave system. Moreover, the newly proposed control scheme is applied to implement synchronization of fractional-order Duffing-Holmes system. The simulation results demonstrate that the backstepping SMC method is robust against the modeling uncertainties and external disturbances.

A Robust Control Approach for Primary Frequency Regulation through Variable Speed Wind Turbines

2010 ◽  
Vol 130 (11) ◽  
pp. 1002-1009 ◽  
Author(s):  
Jorge Morel ◽  
Hassan Bevrani ◽  
Teruhiko Ishii ◽  
Takashi Hiyama
Keyword(s):  
Robust Control ◽  
Wind Turbines ◽  
Frequency Regulation ◽  
Variable Speed ◽  
Control Approach ◽  
Primary Frequency
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