Recursive delayed feedback control for chaotic discrete-time systems

2003 ◽  
Author(s):  
S. Yamamoto ◽  
T. Hino ◽  
T. Ushio
Keyword(s):  
Feedback Control ◽  
Discrete Time ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Discrete Time Systems ◽  
Time Systems

STABILIZATION OF UNSTABLE PERIODIC ORBITS OF CHAOTIC DISCRETE-TIME SYSTEMS USING PREDICTION-BASED FEEDBACK CONTROL

2002 ◽  
Vol 12 (02) ◽  
pp. 439-446 ◽  
Author(s):  
TORU HINO ◽  
SHIGERU YAMAMOTO ◽  
TOSHIMITSU USHIO
Keyword(s):  
Fixed Point ◽  
Feedback Control ◽  
Periodic Orbits ◽  
Discrete Time ◽  
Delayed Feedback Control ◽  
Necessary Condition ◽  
Unstable Periodic Orbits ◽  
Discrete Time Systems ◽  
Unstable Fixed Point ◽  
Time Systems

In this paper, we consider feedback control that stabilizes unstable periodic orbits (UPOs) of chaotic discrete-time systems. First, we show that there exists a strong necessary condition for stabilization of the UPOs when we use delayed feedback control (DFC) that is known as one of the useful methods for controlling chaotic systems. The condition is similar to that in the fixed point stabilization problem, in which it is impossible to stabilize the target unstable fixed point if the Jacobian matrix of the linearized system around it has an odd number of real eigenvalues greater than unity. In order to stabilize UPOs which cannot be stabilized by the standard DFC, we adopt prediction-based control. We show a necessary and sufficient condition for the stabilization of the UPOs with arbitrary period.

Sign in / Sign up

Export Citation Format

Share Document