A Frequency Domain Condition for Boundedness of Learning Control Using a Forgetting Factor

2006 ◽  
Author(s):  
Yasumasa Fujisaki ◽  
Fuminori Kato
Keyword(s):  
Frequency Domain ◽  
Learning Control ◽  
Forgetting Factor ◽  
Domain Condition

A Frequency Domain Analysis of Learning Control

1994 ◽  
Vol 116 (4) ◽  
pp. 781-786 ◽  
Author(s):  
C. J. Goh
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Linear Time ◽  
Planning Horizon ◽  
Time Domain Analysis ◽  
Learning Control ◽  
Domain Analysis ◽  
Frequency Domain Analysis ◽  
Convergence Criterion ◽  
The Time Domain

The convergence of learning control is traditionally analyzed in the time domain. This is because a finite planning horizon is often assumed and the analysis in time domain can be extended to time-varying and nonlinear systems. For linear time-invariant (LTI) systems with infinite planning horizon, however, we show that simple frequency domain techniques can be used to quickly derive several interesting results not amenable to time-domain analysis, such as predicting the rate of convergence or the design of optimum learning control law. We explain a paradox arising from applying the finite time convergence criterion to the infinite time learning control problem, and propose the use of current error feedback for controlling possibly unstable systems.

PD-Type ILC Algorithm Research with Forgetting Factor for a Class of Linear Systems with Multiple Time Delays

2012 ◽  
Vol 220-223 ◽  
pp. 1125-1130 ◽  
Author(s):  
Hong Yang ◽  
Sheng Ming Li
Keyword(s):  
Linear Systems ◽  
Iterative Learning Control ◽  
Time Delays ◽  
Learning Control ◽  
Iterative Learning ◽  
Multiple Time ◽  
Forgetting Factor ◽  
Convergence Conditions ◽  
Multiple Time Delays ◽  
Study Results

Based on iterative learning control (ILC) algorithm with forgetting factor, the thought that the forgetting factor is a function of iteration numbers is proposed in this paper, which has simplified the convergence conditions. And the convergence analysis is given. Then, the study results of this paper are applied to a class of linear systems with multiple time delays and simulation results show that, under the improvements of the convergence conditions and the reasonable choice of forgetting factor function, the PD-type iterative learning control algorithm with forgetting factor applied to the linear systems with multiple time delays in this paper has effectiveness and superiority.

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