Single state feedback stabilization of unified chaotic systems and circuit implementation

Open Physics ◽  
2014 ◽  
Vol 13 (1) ◽  
Author(s):  
Chun-Guo Jing ◽  
Ping He ◽  
Tao Fan ◽  
Yangmin Li ◽  
Changzhong Chen ◽  
...  
Keyword(s):  
Chaotic System ◽  
State Feedback ◽  
Chaotic Systems ◽  
Feedback Stabilization ◽  
State Feedback Control ◽  
Uncertain Parameter ◽  
Circuit Implementation ◽  
Unified Chaotic System ◽  
Unified Chaotic Systems ◽  
Single State

AbstractThis paper focuses on the single state feedback stabilization problem of unified chaotic system and circuit implementation. Some stabilization conditions will be derived via the single state feedback control scheme. The robust performance of controlled unified chaotic systems with uncertain parameter will be investigated based on maximum and minimum analysis of uncertain parameter, the robust controller which only requires information of a state of the system is proposed and the controller is linear. Both the unified chaotic system and the designed controller are synthesized and implemented by an analog electronic circuit which is simpler because only three variable resistors are required to be adjusted. The numerical simulation and control in MATLAB/Simulink is then provided to show the effectiveness and feasibility of the proposed method which is robust against some uncertainties. The results presented in this paper improve and generalize the corresponding results of recent works.

PRACTICAL SYNCHRONIZATION OF NONAUTONOMOUS SYSTEMS WITH UNCERTAIN PARAMETER MISMATCH VIA A SINGLE STATE FEEDBACK CONTROL

2012 ◽  
Vol 23 (11) ◽  
pp. 1250073 ◽  
Author(s):  
MIHUA MA ◽  
JIN ZHOU ◽  
JIANPING CAI
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
State Feedback Control ◽  
Uncertain Parameter ◽  
Van Der Pol Oscillator ◽  
Control Technique ◽  
Parameter Mismatch ◽  
Nonautonomous Systems ◽  
Approximate Differentiation ◽  
Single State

Robust practical synchronization of general second-order nonautonomous systems with uncertain parameter mismatch is investigated by using a single state feedback control. Some simple general algebraic criteria are derived based on practical stability theory of nonautonomous dynamical system. A distinctive feature of this work is that the parameter mismatch not only exists in system parameters, but also in the external excitation ones. More reasonably, the values of parameter mismatch can be uncertain. Besides, a single state feedback control including an approximate differentiation filter only needs to know information about one state, which provides an advantage over the use of full-state model-based observers. It is shown that the approaches developed here further extend the ideas and techniques presented in recent literature. As a direct application of the new theoretical results, the obtained results are applied to a typical horizontal platform system and the representative forced Duffing–Van der Pol oscillator. Subsequently, numerical simulations demonstrate the effectiveness of the criteria and the robustness of the control technique.

scholarly journals Robust Synchronization of the Unified Chaotic System

2015 ◽  
Vol 5 (1) ◽  
pp. 102
Author(s):  
Hatem Trabelsi ◽  
Mohamed Benrejeb
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Synchronization Control ◽  
Compound Matrices ◽  
Synchronization Problem ◽  
Unified Chaotic System ◽  
Unified Chaotic Systems ◽  
Robust Synchronization ◽  
Control Scheme ◽  
Unknown System

<p>The paper investigates the synchronization problem of the unified chaotic system. The case of identical, but unknown master and slave unified chaotic systems is considered. Based on compound matrices formalism, a unified synchronization control scheme is proposed independently of the unknown system parameter. Simulation results are provided to show the effectiveness of the presented scheme.</p>

Sampled-Data State Feedback Stabilization of Boolean Control Networks

2016 ◽  
Vol 28 (4) ◽  
pp. 778-799 ◽  
Author(s):  
Yang Liu ◽  
Jinde Cao ◽  
Liangjie Sun ◽  
Jianquan Lu
Keyword(s):  
State Feedback ◽  
Sufficient Conditions ◽  
Feedback Stabilization ◽  
Necessary And Sufficient Conditions ◽  
State Feedback Control ◽  
Global Stabilization ◽  
Sampled Data ◽  
Control Networks ◽  
Piecewise Constant Control ◽  
Necessary And Sufficient

In this letter, we investigate the sampled-data state feedback control (SDSFC) problem of Boolean control networks (BCNs). Some necessary and sufficient conditions are obtained for the global stabilization of BCNs by SDSFC. Different from conventional state feedback controls, new phenomena observed the study of SDSFC. Based on the controllability matrix, we derive some necessary and sufficient conditions under which the trajectories of BCNs can be stabilized to a fixed point by piecewise constant control (PCC). It is proved that the global stabilization of BCNs under SDSFC is equivalent to that by PCC. Moreover, algorithms are given to construct the sampled-data state feedback controllers. Numerical examples are given to illustrate the efficiency of the obtained results.

scholarly journals Composite One- to Six-Scroll Hidden Attractors in a Memristor-Based Chaotic System and Their Circuit Implementation

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Ying Li ◽  
Xiaozhu Xia ◽  
Yicheng Zeng ◽  
Qinghui Hong
Keyword(s):  
Fixed Point ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Circuit Implementation ◽  
Hidden Attractors ◽  
Coexisting Attractors ◽  
Extreme Multistability ◽  
Different Types ◽  
Hardware Circuit ◽  
New System

Chaotic systems with hidden multiscroll attractors have received much attention in recent years. However, most parts of hidden multiscroll attractors previously reported were repeated by the same type of attractor, and the composite of different types of attractors appeared rarely. In this paper, a memristor-based chaotic system, which can generate composite attractors with one up to six scrolls, is proposed. These composite attractors have different forms, similar to the Chua’s double scroll and jerk double scroll. Through theoretical analysis, we find that the new system has no fixed point; that is to say, all of the composite multiscroll attractors are hidden attractors. Additionally, some complicated dynamic behaviors including various hidden coexisting attractors, extreme multistability, and transient transition are explored. Moreover, hardware circuit using discrete components is implemented, and its experimental results supported the numerical simulations results.

New Criteria on Impulsive Stabilization and Synchronization of Delayed Unified Chaotic Systems with Uncertainty

2011 ◽  
Vol 267 ◽  
pp. 450-455
Author(s):  
Yuan Qiang Chen
Keyword(s):  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Matrix Inequality ◽  
Unified Chaotic System ◽  
Unified Chaotic Systems ◽  
Lyapunov Function Method ◽  
Inequality Techniques ◽  
New Criteria ◽  
Synchronization Problems ◽  
Impulsive Stabilization

This paper investigates stability and synchronization problems for delayed unified chaotic system with parameter uncertainty by employing the Lyapunov function method and matrix inequality techniques. Sufficient conditions for their asymptotical stability and synchronization are developed under given impulsive controllers. Finally, the validity of the obtained results is shown by a numerical example and its simulation.

Some New Dissipative Chaotic Systems with Cyclic Symmetry

2018 ◽  
Vol 28 (13) ◽  
pp. 1850164 ◽  
Author(s):  
Karthikeyan Rajagopal ◽  
Shirin Panahi ◽  
Anitha Karthikeyan ◽  
Ahmed Alsaedi ◽  
Viet-Thanh Pham ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Stability Analysis ◽  
Lyapunov Exponent ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Basin Of Attraction ◽  
Cyclic Symmetry ◽  
Circuit Implementation ◽  
New Chaotic System ◽  
The Basin Of Attraction

Designing new chaotic system with specific features is an interesting field in nonlinear dynamics. In this paper, some new chaotic systems with cyclic symmetry are proposed. In order to understand the overall behavior of such systems, the dynamical analyses such as stability analysis, bifurcation and Lyapunov exponent analysis are done. The accurate examination of bifurcation plot represents that these systems are multistable which makes them more interesting. Also, the basin of attraction of these systems is investigated to detect the type of attractors of these systems which are self-excited. Finally, the circuit implementation is carried out to show their feasibility.

Sign in / Sign up

Export Citation Format

Share Document