DELAYED FEEDBACK CONTROL OF CHAOTIC SYSTEMS WITH DRY FRICTION

2002 ◽  
Vol 12 (08) ◽  
pp. 1877-1883 ◽  
Author(s):  
UGO GALVANETTO
Keyword(s):  
Dry Friction ◽  
Chaotic Systems ◽  
Control Method ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Chaotic Attractors ◽  
Unstable Periodic Orbits ◽  
Numerical Techniques ◽  
The Stability ◽  
Time Delayed Feedback

This paper describes some numerical techniques to control unstable periodic orbits embedded in chaotic attractors of a particular discontinuous mechanical system. The control method is a continuous time delayed feedback that modifies the stability of the orbit but does not affect the orbit itself.

scholarly journals A NEW GENERALIZATION OF DELAYED FEEDBACK CONTROL

2009 ◽  
Vol 19 (01) ◽  
pp. 365-377 ◽  
Author(s):  
ÖMER MORGÜL
Keyword(s):  
Periodic Orbits ◽  
Chaotic Systems ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Stabilization Problem ◽  
Unstable Periodic Orbits ◽  
One Dimensional ◽  
Feedback Scheme ◽  
The Stability ◽  
Stability Results

In this paper, we consider the stabilization problem of unstable periodic orbits of one-dimensional discrete time chaotic systems. We propose a novel generalization of the classical delayed feedback law and present some stability results. These results show that for period 1 all hyperbolic periodic orbits can be stabilized by the proposed method; for higher order periods the proposed scheme possesses some inherent limitations. However, some more improvement over the classical delayed feedback scheme can be achieved with the proposed scheme. The stability proofs also give the possible feedback gains which achieve stabilization. We will also present some simulation results.

MASTER-SLAVE SYNCHRONIZATION OF NONAUTONOMOUS CHAOTIC SYSTEMS AND ITS APPLICATION TO ROTATING PENDULUMS

2012 ◽  
Vol 22 (06) ◽  
pp. 1250147 ◽  
Author(s):  
KE DING ◽  
QING-LONG HAN
Keyword(s):  
Chaotic Systems ◽  
Design Method ◽  
Sufficient Conditions ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Phase Locked Loops ◽  
Linear Matrix ◽  
Delayed Feedback Controller ◽  
Delay Dependent ◽  
Time Delayed Feedback

Some mathematical models in engineering and physics, such as rotating pendulums, governors and phase locked loops in circuits, can be described as nonautonomous systems in which there exist chaotic attractors. This paper investigates master-slave synchronization for two nonautonomous chaotic systems by using time-delayed feedback control. Firstly, three delay-dependent synchronization criteria, which are formulated in the form of linear matrix inequalities (LMIs), are established for complete synchronization, lag synchronization and anticipating synchronization, respectively. Secondly, sufficient conditions on the existence of a time-delayed feedback controller are derived by employing these newly-obtained synchronization criteria. The controller gain can be obtained by solving a set of LMIs. Finally, the synchronization criteria and the design method are applied to master-slave synchronization for rotating pendulum systems.

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