Adaptive iterative learning control for unknown linear time-varying continuous systems

Abstract

This paper presents a novel model reference adaptive iterative learning control (ILC) for unknown continuous-time linear time-varying systems. The unknown time-varying parameters of the system are neither required to vary slowly nor to have known bounds. The system is not required to be minimum-phase, stable, controllable or observable. The input of the system is determined by a differentiator-free control law. The used reference model is time-invariant and first order and thus choosing its parameters is easily possible, even though, the system under control is high order and time variant. Almost all of the components of the system initial condition can be iteration variant. By introducing a novel kind of Lyapunov function the convergence of the proposed adaptive ILC (AILC) and achieving asymptotic tracking are proved. Also, by rigorous mathematical analysis and with the help of some mathematical key techniques such as Bellman-Gronwall lemma, it is shown that all signals and quantities in the closed-loop system are bounded in the sense of at least one norm. Finally, the effectiveness of the proposed method is verified by two simulation examples.

Stabilization of two-dimensional mixed continuous-discrete-time systems via dynamic output feedback with application to iterative learning control design

“…This is because in ILC two independent variables exist, where one of the variables is time and the other one is repetition number. The interested readers are referred to Ahn et al (2007), Xu (2011), Bouakrif and Zasadzinski (2018), Shen (2018), Afsharnia et al (2019), Bensidhoum et al (2019), Jonnalagadda et al (2020) and references therein in order to see the concepts and applications of ILC, and see Geng et al (1990), Owens et al (2000), Li et al (2005a), Hladowski et al (2010), Meng et al (2010), Guan et al (2014) and Wang et al (2017b) for the usage of 2-D systems theory in ILC design.…”

Neural iterative learning identifier‐based iterative learning controller for time‐varying nonlinear systems

“…In this section, we present the proposed NILI for the underlying dynamic system (1). Equation ( 1) can be rewritten as follows:…”

“…Theorem 1. Consider system (1), and assume Assumption 1 is satisfied, the proposed neural network ( 7) is proposed as an iterative learning identifier for (1). Using iterative updating laws ( 18) and ( 19), the convergence of the proposed NILI is guaranteed such that for t = 0,1,…,N, lim…”

“…Also, iterative updating laws are the same as Equations ( 18) and (19). Now, we propose a new NILI-based ILC for system (1)…”

“…Iterative learning control (ILC) is a useful control method for unknown or uncertain dynamical systems that repeat a task in a finite time interval repetitively. In the ILC algorithm, the information from previous iterations is used to modify the control input of the system until defined control aim is achieved [1][2][3][4][5]. One can see several studies [6][7][8][9] for detailed concept, recent developments, and applied fields of ILC.…”