Finite-time generalized function matrix projective lag synchronization of coupled dynamical networks with different dimensions via the double power function nonlinear feedback control method

2014 ◽  
Vol 89 (7) ◽  
pp. 075204 ◽  
Author(s):  
Hao Dai ◽  
Gangquan Si ◽  
Lixin Jia ◽  
Yanbin Zhang
Keyword(s):  
Finite Time ◽  
Control Method ◽  
Generalized Function ◽  
Nonlinear Feedback Control ◽  
Nonlinear Feedback ◽  
Lag Synchronization ◽  
Feedback Control Method ◽  
Different Dimensions ◽  
Projective Lag Synchronization ◽  
Function Matrix

Approximate Finite-Time Stable Control for Simple Interconnected Power Systems

2013 ◽  
Vol 846-847 ◽  
pp. 305-308
Author(s):  
Jian Li Zhao ◽  
Bao Feng Yan ◽  
Bo Chen
Keyword(s):  
Power Systems ◽  
Finite Time ◽  
Control Method ◽  
Nonlinear Feedback Control ◽  
Nonlinear Feedback ◽  
Extended State ◽  
Interconnected Power Systems ◽  
Feedback Control Method ◽  
Simulation Results ◽  
Stable Control

Considering the simple interconnected power systems, the finite-time stable control problem is studied. A nonlinear feedback control method with dynamic active compensation is proposed, which makes the systems achieves approximately the finite-time stable control. Meantime, in order to solve the problem of system uncertainty and unmeasurable states, an extended state observer is designed. Simulation results show the effectiveness of the control method.

CONTROLLING UNCERTAIN VAN DER POL OSCILLATOR VIA ROBUST NONLINEAR FEEDBACK CONTROL

2004 ◽  
Vol 14 (05) ◽  
pp. 1671-1681 ◽  
Author(s):  
MAO-YIN CHEN ◽  
ZHENG-ZHI HAN ◽  
YUN SHANG ◽  
GUANG-DENG ZONG
Keyword(s):  
Feedback Control ◽  
Control Method ◽  
Reference Signal ◽  
Variable Structure ◽  
Van Der Pol Oscillator ◽  
Nonlinear Feedback Control ◽  
Nonlinear Feedback ◽  
Van Der Pol ◽  
Feedback Control Method ◽  
System Uncertainties

Combining the backstepping design and the variable structure control, we propose a robust nonlinear feedback control method to control an uncertain van der Pol oscillator even if there exist system uncertainties and external disturbances in this oscillator. If system uncertainties are estimated and some parameters are chosen suitably, the output of van der Pol osicllator can track arbitrary smooth reference signal. Theoretical analysis and numerical simulations verify the effectiveness of this method.

Continuous adaptive finite-time modified function projective lag synchronization of uncertain hyperchaotic systems

2016 ◽  
Vol 40 (3) ◽  
pp. 853-860 ◽  
Author(s):  
Xuan-Toa Tran ◽  
Hee-Jun Kang
Keyword(s):  
Finite Time ◽  
Control Method ◽  
Sliding Mode ◽  
External Disturbances ◽  
Lag Synchronization ◽  
Terminal Sliding Mode ◽  
Nonsingular Terminal Sliding Mode ◽  
Projective Lag Synchronization ◽  
Twisting Algorithm ◽  
Hyperchaotic Systems

This paper introduces an adaptive control method for finite-time modified function projective lag synchronization of uncertain hyperchaotic systems. Based upon novel nonsingular terminal sliding mode surfaces and the adaptive super-twisting algorithm, a controller is proposed to provide robustness, high precision and fast and finite-time modified function projective lag synchronization without the knowledge of the upper bound of uncertainties and unknown external disturbances. In addition, chattering is significantly attenuated due to the inherited continuity of the proposed controller. The global stability and finite-time convergence are rigorously proven. Numerical simulation is presented to demonstrate the effectiveness and feasibility of the proposed strategy and to verify the theoretical results.

Projective lag synchronization in drive-response dynamical networks

2014 ◽  
Vol 25 (11) ◽  
pp. 1450068 ◽  
Author(s):  
Ghada Al-Mahbashi ◽  
Mohd Salmi Md Noorani ◽  
Sakhinah Abu Bakar
Keyword(s):  
Chaotic Systems ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Scaling Factor ◽  
Lag Synchronization ◽  
Dynamical Networks ◽  
Feedback Control Method ◽  
Projective Lag Synchronization ◽  
Error Dynamics ◽  
The Stability

This paper investigates projective lag synchronization (PLS) behavior between chaotic systems in drive-response dynamical networks (DRDNs) model with nonidentical nodes. A hybrid feedback control method is designed to achieve the PLS with and without mismatched terms. Specially, the coupling matrix in this model is not assumed to be symmetric, diffusive or irreducible. The stability of the error dynamics is proven theoretically using the Lyapunov stability theory. Finally, analytical results show that the states of the dynamical network with non-delayed coupling can be asymptotically synchronized onto a desired scaling factor under the designed controller. Moreover, the numerical simulations results demonstrate the validity of the proposed method.

A general method for projective-lag synchronization of heterogeneous chaotic maps with different dimensions

2021 ◽  
pp. 107754632110264
Author(s):  
Cun-Fang Feng ◽  
Hai-Jun Yang ◽  
Cai Zhou
Keyword(s):  
Discrete Time ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Control Method ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Lag Synchronization ◽  
Different Dimensions ◽  
Projective Lag Synchronization ◽  
General Method

Projective-lag synchronization of complex systems has attracted much attention in the past two decades. However, the majority of previous studies concentrated on continuous-time chaotic systems or discrete-time chaotic systems with the same dimensions. In our present study, a general method for projective-lag synchronization of different discrete-time chaotic systems characterized with different dimensions is first demonstrated. On the basis of stability theory of discrete-time dynamical systems and Lyapunov stability theory, general controllers are designed by using the active control method. The method could achieve projective-lag synchronization in both cases: [Formula: see text] and [Formula: see text]. The effectiveness and feasibility of the proposed method is demonstrated by the projective-lag synchronization between two-dimensional Lorenz discrete-time system and three-dimensional Stefanski map, as well as between the three-dimensional generalized Hénon map and the two-dimensional quadratic map, respectively.

scholarly journals Adaptive Modified Function Projective Lag Synchronization of Memristor-Based Five-Order Chaotic Circuit Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Qiaoping Li ◽  
Sanyang Liu
Keyword(s):  
Control Method ◽  
Scaling Function ◽  
Control Law ◽  
Chaotic Circuit ◽  
Lmi Approach ◽  
Lag Synchronization ◽  
Bounded Disturbances ◽  
Projective Lag Synchronization ◽  
Adaptive Control Law ◽  
Function Matrix

The modified function projective lag synchronization of the memristor-based five-order chaotic circuit system with unknown bounded disturbances is investigated. Based on the LMI approach and Lyapunov stability theorem, an adaptive control law is established to make the states of two different memristor-based five-order chaotic circuit systems asymptotically synchronized up to a desired scaling function matrix, while the parameter controlling strength update law is designed to estimate the parameters well. Finally, the simulation is put forward to demonstrate the correctness and effectiveness of the proposed methods. The control method involved is simple and practical.

scholarly journals IMPROVEMENT OF POWER SUPPLY ELECTROMAGNETIC COMPATIBILITY BY EXTENSION OF CHAOS ANTICONTROL

2005 ◽  
Vol 14 (04) ◽  
pp. 757-770 ◽  
Author(s):  
CRISTINA MOREL ◽  
MARC BOURCERIE ◽  
FRANÇOIS CHAPEAU-BLONDEAU
Keyword(s):  
Electromagnetic Compatibility ◽  
Control Method ◽  
Power Supplies ◽  
Switching Frequency ◽  
Nonlinear Feedback Control ◽  
Nonlinear Feedback ◽  
Spectral Emission ◽  
Simple Method ◽  
Switch Mode ◽  
Feedback Control Method

Switch-mode power supplies usually emit electromagnetic interferences at the switching frequency and its harmonics. Inducing chaos in these systems has recently been suggested as a means of reducing these spectral emissions, yet at the expense of aggravating the overall magnitude of the ripple in the output voltage. We propose here a new nonlinear feedback control method, which induces chaos, and which is able at the same time to achieve low spectral emission and to maintain a small ripple in the output. The feasibility and usefulness of this new and simple method is shown here with a numerical example, which includes a comparison with the previous control method.

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