An iterative learning controller with initial state learning

Abstract

In iterative learning control (ILC), a common assumption is that the initial states in each repetitive operation should be inside a given ball centered at the desired initial states which may be unknown. This assumption is critical to the stability analysis, and the size of the ball will directly affect the final output trajectory tracking errors. In this paper, this assumption is removed by using an initial state learning scheme together with the traditional D-type ILC updating law. Both linear and nonlinear time-varying uncertain systems are investigated. Uniform bounds for the final tracking errors are obtained and these bounds are only dependent on the system uncertainties and disturbances, yet independent of the initial errors. Furthermore, the desired initial states can be identified through learning iterations.

Robust Iterative Learning Control Design: Application to a Robot Manipulator

“…ILC was initially developed as a feedforward action applied directly to the open-loop system [2], [3], [6]. Several closed-loop ILC schemes were later developed in order to benefit from the feedback properties in the first iteration, e.g., [1], [7], [11], [15], and [22].…”

Fuzzy PID Iterative learning control for a class of Nonlinear Systems with Arbitrary Initial Value

“…Chen [3] for a given iterative learning control system for the initial value of the problem, through the system input and initialize the system to achieve the same time iterative tracking. Sun Mingxuan et al [4] discussed the problem of convergence for a given D-type PD-type iterative control system when the initial value of the system is biased. Ren Xuemei, etc.…”

Robot visual servoing with iterative learning control

“…; z=(z 0 1)) is a positive real discrete transfer matrix with a pole at z = 1. Therefore, (6) or (10) where a = e 0=T is a constant satisfying 0 < a < 1.…”

“…The learning law (6) or (13) where Y (x) 2 R n2m is a known nonlinear matrix, f(t; i) 2 R n and a(t; i) 2 R m are unknown vectors but have the repetitive property, i.e., f(t; i) = f(t) and a(t; i) = a(t), we can also obtain the following learning law to meet the upper bounded condition of Theorem 1:…”

“…One of known problem existing in the ILC is the influence of the initial error. Some researchers have studied this problem [4]- [6]. The results show that the final tracking performances are related to the initial error or depend on initial state learning.…”