An Improved Method for Calculating Iterative Learning Control Convergence Rate

2008 ◽  
Author(s):  
Kira Barton ◽  
Andrew Alleyne ◽  
Doug Bristow
Keyword(s):  
Convergence Rate ◽  
Iterative Learning Control ◽  
Learning Algorithm ◽  
Linear Time ◽  
Learning Control ◽  
Iterative Learning ◽  
Arnoldi Method ◽  
Dynamic Simulations ◽  
Large Matrix ◽  
Implicitly Restarted Arnoldi

In Iterative Learning Control (ILC), the lifted system is often used in design and analysis to determine convergence rate of the learning algorithm. Computation of the convergence rate in the lifted setting requires construction of large NxN matrices, where N is the number of data points in an iteration. The convergence rate computation is O(N2) and is typically limited to short iteration lengths because of computational memory constraints. In this article, we present an alternative method for calculating the convergence rate without the need of large matrix calculations. This method uses the implicitly restarted Arnoldi method and dynamic simulations to calculate the ILC norm, reducing the calculation to O(N). In addition to faster computation, we are able to calculate the convergence rate for long iteration lengths. This method is presented for multi-input multi-output, linear time-varying discrete-time systems.

scholarly journals Robust Conditions for Iterative Learning Control in State Feedback and Output Injection Paradigm

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Muhammad A. Alsubaie ◽  
Mubarak KH. Alhajri ◽  
Tarek S. Altowaim ◽  
Salem H. Salamah
Keyword(s):  
Iterative Learning Control ◽  
State Feedback ◽  
Linear Time ◽  
Stability Margin ◽  
Learning Control ◽  
Iterative Learning ◽  
Delay Model ◽  
Linear Time Invariant ◽  
System Input ◽  
Linear Time Invariant Systems

A robust Iterative Learning Control (ILC) design that uses state feedback and output injection for linear time-invariant systems is reintroduced. ILC is a control tool that is used to overcome periodic disturbances in repetitive systems acting on the system input. The design basically depends on the small gain theorem, which suggests isolating a modeled disturbance system and finding the overall transfer function around the delay model. This assures disturbance accommodation if stability conditions are achieved. The reported design has a lack in terms of the uncertainty issue. This study considered the robustness issue by investigating and setting conditions to improve the system performance in the ILC design against a system’s unmodeled dynamics. The simulation results obtained for two different systems showed an improvement in the stability margin in the case of system perturbation.

A New Iterative Learning Control Scheme for Linear Time-varying Discrete Systems

2007 ◽  
Vol 40 (14) ◽  
pp. 279-282 ◽  
Author(s):  
Lukasz Hladowski ◽  
Krzysztof Galkowski ◽  
Eric Rogers ◽  
Paul L. Lewin ◽  
Christopher T. Freeman
Keyword(s):  
Iterative Learning Control ◽  
Linear Time ◽  
Discrete Systems ◽  
Learning Control ◽  
Iterative Learning ◽  
Time Varying ◽  
Control Scheme

Iterative Learning Control for a Class of Modeling Undesirable Single Degree of Freedom System

2014 ◽  
Vol 538 ◽  
pp. 379-382
Author(s):  
Wei Zhou ◽  
Bao Bin Liu
Keyword(s):  
Iterative Learning Control ◽  
Learning Algorithm ◽  
Learning Control ◽  
Iterative Learning ◽  
Degree Of Freedom ◽  
Control Input ◽  
Convergence Properties ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Simulation Results

A class of modeling undesirable single degree of freedom system is studied by using iterative learning control. The proposed iterative learning algorithm constantly updates the control input according to output error until the desired output occurred. So the system with designed controller can achieve perfect accuracy. We have proved convergence properties in iteration domain and simulation results demonstrate the effectiveness of the presented method.

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