scholarly journals Linear feedback control of nonlinear systems with a dominating conservative quadratic term

1998 ◽  
Vol 21 (3) ◽  
pp. 507-518
Author(s):  
Anil Bose ◽  
Alan Cover ◽  
James Reneke
Keyword(s):  
Feedback Control ◽  
Nonlinear Systems ◽  
System Application ◽  
Dissipative System ◽  
Linear Feedback ◽  
Quadratic Term ◽  
Linear Feedback Control ◽  
Feedback Controls

Conditions are investigated for systems of the formMx′=N+Ax+f(x), wherefis quadratic, which lield a point dissipative system. Application of the conditions are made to the problem of existence of linear feedback controlsu=Kxfor systems of the formMx′=N+Ax+f(x)+Buwhich force the system to be point dissipative. The basic results have eztensions to more general classes of systems.

A note on polynomial chaos expansions for designing a linear feedback control for nonlinear systems

2016 ◽  
Vol 87 (3) ◽  
pp. 1653-1666 ◽  
Author(s):  
Mateus de Freitas Virgílio Pereira ◽  
José Manoel Balthazar ◽  
Davi Antônio dos Santos ◽  
Angelo Marcelo Tusset ◽  
Davi Ferreira de Castro ◽  
...  
Keyword(s):  
Feedback Control ◽  
Nonlinear Systems ◽  
Polynomial Chaos ◽  
Linear Feedback ◽  
Linear Feedback Control ◽  
Polynomial Chaos Expansions

Control of the Hopf Bifurcation by a Linear Feedback Control

2015 ◽  
Vol 25 (01) ◽  
pp. 1550006 ◽  
Author(s):  
J. A. López-Renteria ◽  
F. Verduzco ◽  
B. Aguirre-Hernández
Keyword(s):  
Hopf Bifurcation ◽  
Feedback Control ◽  
Nonlinear Systems ◽  
State Feedback ◽  
State Feedback Control ◽  
Linear Feedback ◽  
Linear Feedback Control ◽  
Linear State

In this work, we design a kind of linear state feedback control, via the roots connecting-curve, for a class of nonlinear systems which permits to control the Hopf bifurcation. An illustrative example is given.

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.

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.

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