Adaptive iterative learning control for a class of non-linearly parameterised systems with input saturations

Abstract

In this paper, an adaptive iterative learning control scheme is proposed for a class of non-linearly parameterised systems with unknown time-varying parameters and input saturations. By incorporating a saturation function, a new iterative learning control mechanism is presented which includes a feedback term and a parameter updating term. Through the use of parameter separation technique, the non-linear parameters are separated from the non-linear function and then a saturated difference updating law is designed in iteration domain by combining the unknown parametric term of the local Lipschitz continuous function and the unknown time-varying gain into an unknown time-varying function. The analysis of convergence is based on a time-weighted Lyapunov-Krasovskii-like composite energy function which consists of time-weighted input, state and parameter estimation information. The proposed learning control mechanism warrants a L 2 [0,T ] convergence of the tracking error sequence along the iteration axis. Simulation results are provided to illustrate the effectiveness of the adaptive iterative learning control scheme.

Distributed Robust Adaptive Learning Coordination Control for High-Order Nonlinear Multi-Agent Systems With Input Saturation

“…In turn, the finiteness ofĒ k is followed. From (17) and (21), we can acquire that σ k δ and F k 1 are uniformly bounded, then the finiteness of δ k s is gained, s = 1, 2, . .…”

“…Iterative learning control (ILC) is an effective approach to realize accurate tracking performance under the repetitive environment [14], [15]. ILC for an individual system, [16] designed an ILC algorithm for the uncertain nonlinear systems having IS, and [17]- [19] proposed the adaptive ILC method for non-linearly parameterised systems having IS. Nevertheless, the results of [16]- [19] having IS were performed under the identical initial conditions (i.i.c) [20] which was a rigorous condition and may not be realized in practice.…”

Distributed iterative learning coordination control for leader–follower uncertain non‐linear multi‐agent systems with input saturation

“…ILC for an individual non‐linear system [28, 29], there are also some papers on input saturation. For instance, an ILC method for a kind of non‐linear uncertain systems with input saturation was designed in [30], and the non‐linearly parametric systems with input saturation were investigated in [31–33]. Moreover, as an important branch of ILC, optimal ILC has been widely investigated in [34–36].…”

An adaptive iterative learning control approach based on disturbance estimation for manipulator system

“…[25][26][27][28] In recent years, AILC method became a popular technique in the control field, which generalized lots of algorithms. The following algorithms were effective to reduce the external disturbances, for instance, Nussbaum function, 29 saturation function, 30 and separation technology. 31 A research developed an AILC method based on a fully saturated adaptive learning term and a time-domain feedback term, which aimed to estimate the uncertainty of the unknown time-varying systems.…”