High-Order Ilc With Initial State Learning for Discrete-Time Delayed Systems

Abstract

This article addresses an iterative learning control (ILC) design for a class of linear discrete-time systems with multiple time delays. In order to improve the tracking performance, we introduce a P-type high-order iterative learning algorithm that makes use of information from several previous iterations. An initial state learning scheme is proposed to eliminate the effect of the initialization error on the final tracking error. Furthermore, we establish a sufficient condition to ensure asymptotic convergence. A simulation example is also provided to illustrate the effectiveness of the proposed result.

High-Order Feedback Iterative Learning Control Algorithm with Forgetting Factor

“…When conditions V = 0 and ‖ (0)‖ = 0 are satisfied, from (17), we get = 0 and from (19), we obtain lim → ∞ ‖ ‖ = 0. Then, (16) gives lim → ∞ ‖ ‖ = 0; we have lim → ∞ ‖ ( )‖ = lim → ∞ ‖ ‖ = 0. According to limit definition, at any bound of given tracking error * , we can choose a group parameter of and G in order to reach the conclusion of this theorem sup ∈[0, ] ‖ ( )‖ ≤ * , with ∀ ≥ .…”

“…If̃≤ ∑ =1̃< 1, then lim → ∞ ≤̃/(1 −̃). By Lemma 3, we choose a sufficiently large constant such that the following inequality holds when conditions̃< 1 and = ∑ =1 < 1 are satisfied: (16), (17), and (19), we get that the tracking error bound converges to a small neighborhood of the origin, as goes to infinity. Meanwhile, the tracking error ‖ ‖ , initial state error ‖ (0)‖ , and the bound of output disturbance item V have a linear relationship.…”

“…However, some ILC algorithm's convergence process is slow. To make the system track expectations more quickly and precisely, a high-order feedback iterative learning control [16] is proposed. Although it is applied to the linear system, the algorithm itself is of great value.…”

High-order model-free adaptive iterative learning control

“…At present, scholars have done a lot of work on high-order ILC. Li et al (2012) proposed a high-order ILC with initial value learning for linear systems. For the possible output measurement data dropout, Bu et al (2011) designed a high-order ILC using the super-vector approach.…”

“…Note that some of the high-order ILCs (Bien and Huh, 1989; Boudria and Gauthier, 2012; Bu et al, 2011; Chen et al, 1997a, 1998; Gunnarsson and NorrlöF, 2006; Li et al, 2012) focus on proportional–integral–derivative (PID)-type control laws, and the control performance is limited by the fixed learning gains that cannot be adapted to change. Beyond that, most of the controller design and analysis are for linear systems (Boudria and Gauthier, 2012; Bu et al, 2011; Chen et al, 1997b; Gunnarsson and NorrlöF, 2006; HäTöNen et al, 2006; Li et al, 2012) or affine nonlinear systems (Bien and Huh, 1989; Chen et al, 1997a, 1998). It is worth pointing out that these methods (Bien and Huh, 1989; Boudria and Gauthier, 2012; Bu et al, 2011; Chen et al, 1997a, 1997b, 1998; Gunnarsson and NorrlöF, 2006; HäTöNen et al, 2006; Li et al, 2012) need to know the model information of the system in actual application.…”