scholarly journals Synchronization of Chaotic Systems: A Generic Nonlinear Integrated Observer-Based Approach

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Muhammad Majid Hussain ◽  
Muhammad Siddique ◽  
Ziyad M. Almohaimeed ◽  
Romaisa Shamshad ◽  
Rizwan Akram ◽  
...  
Keyword(s):  
Chaotic Systems ◽  
Inequality Constraints ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Synchronization Errors ◽  
Nonlinear Properties ◽  
State Approximation ◽  
Approximation Errors ◽  
The Difference ◽  
Neuronal Systems

The purpose of this research is to study the synchronization of two integrated nonlinear systems with time delay and disturbances. A nonlinear system is a system in which the difference in output is not relative to the difference in input. A new control methodology for synchronization of the two chaotic systems master and slave is recognized by means of the unique integrated chaotic synchronous observer and the integrated chaotic adaptive synchronous observer. The instantaneous approximation states of the master and slave systems are accomplished by means of methods for suggesting observers for every one of the master and slave systems and by the production of error signals between these approximated states. This approximated synchronization error signal and state approximation errors meet at the origin by means of methods involving a particular observer-based feedback control signal to ensure synchronization and state approximation. Using Lyapunov stability theory, adaptive and nonadaptive laws for control systems, and nonlinear properties, the intermingling conditions for state approximation errors and approximated synchronization errors are established as nonlinear matrix inequalities. A solution to the resulting inequality constraints using a two-step linear matrix inequality (LMI)-based approach is introduced, giving essential and adequate conditions to extract values from the controller gain and observer gain matrices. Simulation of the suggested synchronization procedure for FitzHugh–Nagumo neuronal systems is demonstrated to expand the viability of the suggested observer-based control techniques.

Disturbed Chaotic Systems Synchronization via Robust Mixed Functional Projective Method

2014 ◽  
Vol 496-500 ◽  
pp. 1293-1297
Author(s):  
Tao Fan ◽  
Ning Fang ◽  
Fei Tan
Keyword(s):  
State Feedback ◽  
Chaos Control ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Generalized Synchronization ◽  
Linear State ◽  
Control And Synchronization

Robust mixed functional projective synchronization (RMFPS), which is the generalized synchronization idea developed very recently, is investigated in this paper. Based on Lyapunov stability theory and linear matrix inequality (LMI), some novel stability criterions for the synchronization between drive and response chaotic systems with disturbances are derived, and then a simple linear state feedback synchronization controller is designed. In order to test the proposed method, numerical simulations of hyper-chaotic unified systems with disturbances are then provided to show the effectiveness and feasibility of this chaos control and synchronization schemes.

H∞ SYNCHRONIZATION OF SWITCHED CHAOTIC SYSTEMS AND ITS APPLICATION TO SECURE COMMUNICATIONS

2012 ◽  
Vol 22 (03) ◽  
pp. 1250058 ◽  
Author(s):  
ZHANG-LIN WAN ◽  
TEH-LU LIAO ◽  
YI-YOU HOU ◽  
JUN-JUH YAN
Keyword(s):  
Communication Systems ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Optimization Techniques ◽  
Linear Matrix ◽  
Secure Communications ◽  
Switching Law ◽  
Synchronization Problem ◽  
Matrix Equality ◽  
Security Communication

This paper deals with the H∞ synchronization problem of switched chaotic systems accompanied by a time-driven switching law and its application to secure communications. Based on the Lyapunov stability theory and linear matrix inequality (LMI) and linear matrix equality (LME) optimization techniques, an output feedback controller that guarantees the synchronization of switched master-slave chaotic systems is designed. A chaotic encryption technique that uses synchronization is proposed for securely transmitting a message over public channels. Numerical simulations of both analog and digital security communication systems are conducted to demonstrate the effectiveness of the proposed methods.

scholarly journals Chaos Synchronization Based on Unknown Input Proportional Multiple-Integral Fuzzy Observer

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
T. Youssef ◽  
M. Chadli ◽  
H. R. Karimi ◽  
M. Zelmat
Keyword(s):  
Secure Communication ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Multiple Integral ◽  
Linear Matrix ◽  
Unknown Input ◽  
Matrix Inequalities ◽  
Decision Variables ◽  
Takagi Sugeno

This paper presents an unknown input Proportional Multiple-Integral Observer (PIO) for synchronization of chaotic systems based on Takagi-Sugeno (TS) fuzzy chaotic models subject to unmeasurable decision variables and unknown input. In a secure communication configuration, this unknown input is regarded as a message encoded in the chaotic system and recovered by the proposed PIO. Both states and outputs of the fuzzy chaotic models are subject to polynomial unknown input withkth derivative zero. Using Lyapunov stability theory, sufficient design conditions for synchronization are proposed. The PIO gains matrices are obtained by resolving linear matrix inequalities (LMIs) constraints. Simulation results show through two TS fuzzy chaotic models the validity of the proposed method.

Adaptive state estimation of Markov switched neural networks driven by Lévy noise

2019 ◽  
Vol 42 (2) ◽  
pp. 330-336
Author(s):  
Dongbing Tong ◽  
Qiaoyu Chen ◽  
Wuneng Zhou ◽  
Yuhua Xu
Keyword(s):  
Neural Networks ◽  
State Estimation ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Lévy Noise ◽  
Linear Matrix ◽  
Delayed Neural Networks ◽  
Switched Neural Networks ◽  
Inequality Technique ◽  
Levy Noise

This paper proposes the [Formula: see text]-matrix method to achieve state estimation in Markov switched neural networks with Lévy noise, and the method is very distinct from the linear matrix inequality technique. Meanwhile, in light of the Lyapunov stability theory, some sufficient conditions of the exponential stability are derived for delayed neural networks, and the adaptive update law is obtained. An example verifies the condition of state estimation and confirms the effectiveness of results.

A UNIFIED FRAMEWORK FOR SYNCHRONIZATION AND CONTROL OF DYNAMICAL SYSTEMS

1994 ◽  
Vol 04 (04) ◽  
pp. 979-998 ◽  
Author(s):  
CHAI WAH WU ◽  
LEON O. CHUA
Keyword(s):  
Dynamical Systems ◽  
Chaotic Systems ◽  
Main Tool ◽  
Lyapunov Stability Theory ◽  
Asymptotical Stability ◽  
Unified Framework ◽  
Partial Synchronization ◽  
Chua’S Oscillator ◽  
And Control

In this paper, we give a framework for synchronization of dynamical systems which unifies many results in synchronization and control of dynamical systems, in particular chaotic systems. We define concepts such as asymptotical synchronization, partial synchronization and synchronization error bounds. We show how asymptotical synchronization is related to asymptotical stability. The main tool we use to prove asymptotical stability and synchronization is Lyapunov stability theory. We illustrate how many previous results on synchronization and control of chaotic systems can be derived from this framework. We will also give a characterization of robustness of synchronization and show that master-slave asymptotical synchronization in Chua’s oscillator is robust.

SYNCHRONIZING CONTINUOUS TIME CHAOTIC SYSTEMS OVER NONDETERMINISTIC NETWORKS WITH PACKET DROPOUTS

2012 ◽  
Vol 22 (12) ◽  
pp. 1250300 ◽  
Author(s):  
FERNANDO O. SOUZA ◽  
REINALDO M. PALHARES ◽  
EDUARDO M. A. M. MENDES ◽  
LEONARDO A. B. TORRES
Keyword(s):  
Continuous Time ◽  
Chaotic Systems ◽  
Random Fluctuation ◽  
Control Synthesis ◽  
Linear Matrix ◽  
Delayed Systems ◽  
Packet Dropouts ◽  
Time Varying Delay ◽  
Stability And Stabilization ◽  
Varying Delay

The problem of control synthesis for master–slave synchronization of continuous time chaotic systems of Lur'e type using sampled feedback control subject to sampling time random fluctuation and data packet dropouts is investigated. New stability and stabilization conditions are proposed based on Linear Matrix Inequalities (LMIs). The idea is to connect two very efficient approaches to deal with delayed systems: the discretized Lyapunov functional for systems with pointwise delay and the convex analysis for systems with time-varying delay. Simulation examples based on synchronizing coupled Chua's circuits are used to illustrate the effectiveness of the proposed methodology.

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.

scholarly journals HOW CRUCIAL IS SMALL WORLD CONNECTIVITY FOR DYNAMICS?

2006 ◽  
Vol 16 (09) ◽  
pp. 2767-2775 ◽  
Author(s):  
PRASHANT M. GADE ◽  
SUDESHNA SINHA
Keyword(s):  
Spectral Properties ◽  
Chaotic Systems ◽  
Signal To Noise Ratio ◽  
Dynamical Behavior ◽  
Small World ◽  
High Strength ◽  
Nonlocal Coupling ◽  
Small Noise ◽  
Optimal Value ◽  
Neuronal Systems

We study the dynamical behavior of the collective field of chaotic systems on small world lattices. Coupled neuronal systems as well as coupled logistic maps are investigated. We observe that significant changes in dynamical properties occur only at a reasonably high strength of nonlocal coupling. Further, spectral features, such as signal-to-noise ratio (SNR), change monotonically with respect to the fraction of random rewiring, i.e. there is no optimal value of the rewiring fraction for which spectral properties are most pronounced. We also observe that for small rewiring, results are similar to those obtained by adding small noise.

α-Stabilization Criterion for Networked Control Systems

2013 ◽  
Vol 321-324 ◽  
pp. 1858-1862 ◽  
Author(s):  
Li Sheng Wei ◽  
Zhi Hui Mei ◽  
Ming Jiang
Keyword(s):  
Time Delay ◽  
Control Systems ◽  
Optimization Problem ◽  
Networked Control Systems ◽  
Lyapunov Stability Theory ◽  
Networked Control ◽  
Linear Matrix ◽  
Packet Dropout ◽  
Lmi Approach ◽  
Network Transmission

This study focus on α-Stability constraints for uncertain networked control systems (NCSs) subject to disturbance inputs, where the network transmission is connected with time-delay and packet dropout. The overall NCSs model is derived. In order to obtain much less conservative results, the sufficient condition for feasibility is presented in term of 2nd Lyapunov stability theory and a set of linear matrix inequalities (LMIs). This LMI approach can be the optimization problem of computation of the maximal allowed bound on the time-delay for NCSs.

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