scholarly journals Stabilizing equilibrium by linear feedback control for controlling chaos in Chen system

2011 ◽  
Vol 285 ◽  
pp. 012008
Author(s):  
V A Costa ◽  
G A González
Keyword(s):  
Feedback Control ◽  
Linear Feedback ◽  
Linear Feedback Control ◽  
Chen System ◽  
Controlling Chaos

Optimization approach to the constrained regulation problem for linear continuous-time fractional-order systems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Xindong Si ◽  
Hongli Yang
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
State Feedback Control ◽  
Invariant Sets ◽  
Linear Feedback ◽  
Control Law ◽  
Optimization Approach ◽  
Fractional Order Systems ◽  
Linear Feedback Control ◽  
Computational Point

AbstractThis paper deals with the Constrained Regulation Problem (CRP) for linear continuous-times fractional-order systems. The aim is to find the existence conditions of linear feedback control law for CRP of fractional-order systems and to provide numerical solving method by means of positively invariant sets. Under two different types of the initial state constraints, the algebraic condition guaranteeing the existence of linear feedback control law for CRP is obtained. Necessary and sufficient conditions for the polyhedral set to be a positive invariant set of linear fractional-order systems are presented, an optimization model and corresponding algorithm for solving linear state feedback control law are proposed based on the positive invariance of polyhedral sets. The proposed model and algorithm transform the fractional-order CRP problem into a linear programming problem which can readily solved from the computational point of view. Numerical examples illustrate the proposed results and show the effectiveness of our approach.

FREQUENCY-DOMAIN CRITERIA FOR GLOBAL SYNCHRONIZATION OF MULTISCROLL CHAOTIC SYSTEMS UNDER LINEAR FEEDBACK CONTROL

2010 ◽  
Vol 20 (07) ◽  
pp. 2165-2177 ◽  
Author(s):  
XIAOFENG WU ◽  
ZHIFANG GUI ◽  
GUANRONG CHEN
Keyword(s):  
Feedback Control ◽  
Frequency Domain ◽  
Chaotic Systems ◽  
Linear Feedback ◽  
Error Feedback ◽  
Linear Feedback Control ◽  
Global Synchronization ◽  
General Mathematical Model ◽  
Linear State ◽  
Absolute Stability Theory

This paper provides a unified approach for achieving and analyzing global synchronization of a class of master-slave coupled multiscroll chaotic systems under linear state-error feedback control. A general mathematical model for such a class of multiscroll chaotic systems is first established. Based on some special properties of such systems, two less-conservative frequency-domain criteria for the desirable global synchronization are rigorously proven by means of the absolute stability theory. The analysis is then applied to two master-slave coupled modified Chua's circuits, obtaining the corresponding simple and precise algebraic criteria for global synchronization, which are finally verified by numerical simulations.

Empirical parameter correlations for the synthesis of linear feedback control systems

1969 ◽  
Vol 57 (7) ◽  
pp. 1321-1322 ◽  
Author(s):  
V. Seshadri ◽  
V.R. Rao ◽  
C. Eswaran ◽  
S. Eappen
Keyword(s):  
Feedback Control ◽  
Control Systems ◽  
Linear Feedback ◽  
Linear Feedback Control ◽  
Empirical Parameter ◽  
Feedback Control Systems

Master-Slave Global Synchronization for Froude Pendulums via Linear State Error Feedback Control

2013 ◽  
Vol 275-277 ◽  
pp. 2565-2569
Author(s):  
Lin Xu ◽  
Zhong Liu ◽  
Yun Chen
Keyword(s):  
Feedback Control ◽  
Chaos Synchronization ◽  
Linear Feedback ◽  
Error Feedback ◽  
Linear Feedback Control ◽  
Global Synchronization ◽  
Numerical Example ◽  
Linear State ◽  
Synchronization Scheme ◽  
State Error

This paper deals with the global chaos synchronization of master-slave Froude pendulums coupled by linear state error feedback control. A master-slave synchronization scheme of the Froude pendulums under linear feedback control is presented. Based on this scheme, some sufficient criteria for global synchronization are proved and optimized. A numerical example is provided to demonstrate the effectiveness of the criteria obtained.

Double strange attractors in rigid body motion with linear feedback control

1981 ◽  
Vol 86 (2) ◽  
pp. 63-67 ◽  
Author(s):  
R.B. Leipnik ◽  
T.A. Newton
Keyword(s):  
Feedback Control ◽  
Rigid Body ◽  
Rigid Body Motion ◽  
Strange Attractors ◽  
Body Motion ◽  
Linear Feedback ◽  
Linear Feedback Control

scholarly journals Synchronization of Liu chaotic system based on linear feedback control and its experimental verification

2006 ◽  
Vol 55 (10) ◽  
pp. 5055
Author(s):  
Wang Fa-Qiang ◽  
Liu Chong-Xin
Keyword(s):  
Feedback Control ◽  
Chaotic System ◽  
Experimental Verification ◽  
Linear Feedback ◽  
Linear Feedback Control

scholarly journals Controlled Positive Dynamic Systems with an Entropy Operator: Fundamentals of the Theory and Applications

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2585
Author(s):  
Yuri S. Popkov
Keyword(s):  
Feedback Control ◽  
Dynamic Systems ◽  
Dynamic Properties ◽  
Monotone Operators ◽  
Singular Points ◽  
Program Control ◽  
Linear Feedback ◽  
Economic Systems ◽  
Linear Feedback Control ◽  
Nonzero Equilibrium

Controlled dynamic systems with an entropy operator (DSEO) are considered. Mathematical models of such systems were used to study the dynamic properties in demo-economic systems, the spatiotemporal evolution of traffic flows, recurrent procedures for restoring images from projections, etc. Three problems of the study of DSEO are considered: the existence and uniqueness of singular points and the influence of control on them; stability in “large” of the singular points; and optimization of program control with linear feedback. The theorems of existence, uniqueness, and localization of singular points are proved using the properties of equations with monotone operators and the method of linear majorants of the entropy operator. The theorem on asymptotic stability of the DSEO in “large” is proven using differential inequalities. Methods for the synthesis of quasi-optimal program control and linear feedback control with integral quadratic quality functional, and ensuring the existence of a nonzero equilibrium, were developed. A recursive method for solving the integral equations of the DSEO using the multidimensional functional power series and the multidimensional Laplace transform was developed. The problem of managing regional foreign direct investment is considered, the distribution of flows is modeled by the corresponding DSEO. It is shown that linear feedback control is a more effective tool than program control.

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