On the Efficacy of Nonlinear Control in Uncertain Linear Systems

1981 ◽  
Vol 103 (2) ◽  
pp. 95-102 ◽  
Author(s):  
G. Leitmann
Keyword(s):  
Dynamical Systems ◽  
Feedback Control ◽  
Nonlinear Control ◽  
Linear Systems ◽  
Linear Feedback ◽  
System Response ◽  
Linear Feedback Control ◽  
Linear Dynamical Systems ◽  
Uncertain Linear Systems ◽  
Measured State

We consider a class of linear dynamical systems containing uncertain elements and subject to uncertain inputs, and for which either uncertain state or output is available. We construct a feedback control, utilizing measured state or estimated state, which guarantees that every system response is ultimately bounded within a certain neighborhood of the zero state. Performance resulting from use of this control is compared with that due to the use of purely linear feedback control.

Optimal Linear and Nonlinear Control Design for Chaotic Systems

2005 ◽  
Author(s):  
Marat Rafikov ◽  
Jose´ Manoel Balthazar
Keyword(s):  
Feedback Control ◽  
Nonlinear Control ◽  
Chaotic Systems ◽  
Duffing Oscillator ◽  
Sufficient Conditions ◽  
Control Design ◽  
Linear Feedback ◽  
Nonlinear Feedback ◽  
Linear Feedback Control ◽  
Linear And Nonlinear

In this work, the linear and nonlinear feedback control techniques for chaotic systems were been considered. The optimal nonlinear control design problem has been resolved by using Dynamic Programming that reduced this problem to a solution of the Hamilton-Jacobi-Bellman equation. In present work the linear feedback control problem has been reformulated under optimal control theory viewpoint. The formulated Theorem expresses explicitly the form of minimized functional and gives the sufficient conditions that allow using the linear feedback control for nonlinear system. The numerical simulations for the Ro¨ssler system and the Duffing oscillator are provided to show the effectiveness of this method.

Nonlinear Control of Mismatched Uncertain Linear Systems and Application to Control of Aircraft

1984 ◽  
Vol 106 (3) ◽  
pp. 203-210 ◽  
Author(s):  
S. N. Singh ◽  
Antoˆnio A. R. Coelho
Keyword(s):  
Nonlinear Control ◽  
Linear Systems ◽  
Digital Simulation ◽  
System Response ◽  
Nonlinear Controller ◽  
Ultimate Boundedness ◽  
Parameter Variations ◽  
Uncertain Linear Systems ◽  
Analytical Expressions ◽  
Vtol Aircraft

This paper describes an approach to control of nonzero set points of uncertain linear systems based on the theory of ultimate boundedness. We derive a nonlinear control which guarantees that every system response is ultimately bounded within a certain neighborhood of the desired nonzero set point. Analytical expressions for the bounds on variations in parameters for ultimate boundedness are obtained. These results are applied to control of a VTOL aircraft whose time-varying parameters are uncertain. Unlike previous works, arbitrary and fast variations in aircraft parameters are allowed. It is shown that the nonlinear controller is effective for larger variation in parameters than the reduced linear controller. Digital simulation results show that the aircraft can be precisely maneuvered in spite of uncertain parameter variations.

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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