Synchronization Error Estimation and Controller Design for Delayed Lur'e Systems With Parameter Mismatches

2012 ◽  
Vol 23 (10) ◽  
pp. 1551-1563 ◽  
Author(s):  
Wangli He ◽  
Feng Qian ◽  
Qing-Long Han ◽  
Jinde Cao
Keyword(s):  
Error Estimation ◽  
Controller Design ◽  
Synchronization Error ◽  
Lur’E Systems

ROBUST SYNCHRONIZATION OF CHAOTIC LUR'E SYSTEMS VIA REPLACING VARIABLES CONTROL

2006 ◽  
Vol 16 (11) ◽  
pp. 3421-3433 ◽  
Author(s):  
XIAOFENG WU ◽  
MUHONG WANG
Keyword(s):  
Frequency Domain ◽  
Error Bound ◽  
Sufficient Conditions ◽  
Synchronization Error ◽  
Linear Matrix ◽  
Lur’E Systems ◽  
Parameter Mismatch ◽  
Chaotic Lur’E Systems ◽  
Definition Of ◽  
Synchronization Scheme

The sufficient conditions for chaos synchronization of two nonidentical systems by replacing variables control have not been proposed until now. In this paper, synchronization of two chaotic Lur'e systems with parameter mismatch by replacing variables control is studied. First of all, we present a master-slave Lur'e systems synchronization scheme with both parameter mismatch and replacing variables control, and derive a responsive error system for the scheme. A new definition of synchronization with finite L 2-gain is then introduced. Based on the definition, the sufficient synchronization criteria which are in the form of linear matrix inequality (LMI) are proved using a quadratic Lyapunov function. By means of MKY lemma the frequency domain criteria are further derived from the obtained LMIs. These frequency domain criteria are illustrated on the master-slave Chua's circuits with parameter mismatch so that the ranges of the parameters of Chua's circuit are analytically solved in the sense of the synchronization with finite L 2-gain by replacing singe-variable control. The illustrative examples verify that within the ranges of the parameters it is possible to synchronize the master-slave Chua's circuits up to a small synchronization error bound, even the qualitative behaviors of the slave circuit are different from that of the master one, such as the trajectory of the master circuit is chaotic and that of the slave divergent. The relation between the synchronization error bound and parameter mismatch is shown.

Fuzzy resilient control for synchronizing chaotic systems with time-variant delay and external disturbance

2021 ◽  
pp. 2150177
Author(s):  
Weipeng Tai ◽  
Dandan Zuo ◽  
Jing Han ◽  
Jianping Zhou
Keyword(s):  
Chaotic Systems ◽  
Controller Design ◽  
Convex Combination ◽  
External Disturbance ◽  
Synchronization Error ◽  
Disturbance Attenuation ◽  
Resilient Control ◽  
Combination Technique ◽  
Design Scheme ◽  
Error System

This paper focuses on the issue of fuzzy resilient control for synchronizing chaotic systems with time-variant delay and external disturbance. The goal is to design a fuzzy resilient controller with additive gain perturbations to guarantee that not only the drive and response systems are asymptotically synchronized in the absence of external disturbance, but also the synchronization error system has a prescribed disturbance attenuation index under the zero initial condition. By utilizing an appropriate Lyapunov–Krasovskii functional, the Bessel–Legendre inequality, and the reciprocally convex combination technique, a criterion on the stability and [Formula: see text] performance of the synchronization error system is derived. Then, by means of some decoupling methods, a design scheme of the fuzzy resilient controller is developed. Finally, one numerical example is provided to examine the effectiveness of the fuzzy resilient controller design scheme.

Multivariable PD controller design for fast chaos synchronization of Lur'e systems

2007 ◽  
Vol 363 (3) ◽  
pp. 192-196 ◽  
Author(s):  
Guilin Wen ◽  
Qing-Guo Wang ◽  
Yong He ◽  
Zhen Ye
Keyword(s):  
Chaos Synchronization ◽  
Controller Design ◽  
Pd Controller ◽  
Lur’E Systems

scholarly journals Distributed trajectory tracking and formation control without velocity measurements by the notion of prior bounded local neighborhood synchronization error

2020 ◽  
Vol 53 (3-4) ◽  
pp. 577-588 ◽  
Author(s):  
Boxian Lin ◽  
Te Zhang ◽  
Bo Zhu ◽  
Kaiyu Qin
Keyword(s):  
Formation Control ◽  
Controller Design ◽  
Input Saturation ◽  
Parameter Tuning ◽  
Synchronization Error ◽  
Velocity Measurements ◽  
Tracking Errors ◽  
Synchronization Errors ◽  
Parameter Mapping ◽  
Local Neighborhood

This paper investigates the robust consensus tracking and formation control problems of multiple second-order systems having exogenous disturbances and no velocity measurements. To account for the input saturation constraint in controller design, a novel notion of local neighborhood synchronization error is proposed, which is obtained using generalized saturation functions and can be regarded as a nonlinear variation of the well-known linear local neighborhood synchronization error. An important property of the notion is proved and then a continuous distributed controller is designed using it. To improve the robustness of the controller with respect to exogenous disturbance, a disturbance estimator–based design and a simple parameter mapping for parameter tuning are proposed. The resulting error system is proven to be small-signal [Formula: see text] stable and input-to-output stable. In particular, the synchronization errors and tracking errors converge asymptotically to zero if the disturbances converge to some constants. By the parameter mapping, the steady-state synchronization errors and tracking errors can be made arbitrarily small. The control scheme is finally modified to adapt to formation control applications by adding the desired position deviation from the leader’s trajectory. The performance of the scheme is demonstrated by the simulation results.

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