Comments on “Adaptive ILC for a class of discrete-time systems with iteration-varying trajectory and random initial condition”

This note points out some errors in the proof of the asymptotic learning convergence of the tracking error in Chi, Hou and Xu [Chi, R.H., Hou, Z.S., & Xu, J.X. (2008) Adaptive ILC for a class of discrete-time systems with iteration-varying trajectory and random initial condition. Automatica, 44(8), 2207-2213].     

Iterative learning control with input sharing for multi-agent consensus tracking

In this paper, a novel iterative learning control (ILC) scheme with input sharing is presented for multi-agent consensus tracking. In many ILC works for multi-agent coordination problem, each agent maintains its own input learning, and the input signal is corrected by local measurements over iteration domain. If the agents are allowed to share their learned inputs among them, the strategy can improve the learning process as more learning resources are available. In this work, we develop a new type of learning controller by considering the input sharing among agents, which includes the traditional ILC strategy as a special case. The convergence condition is rigorously derived and analyzed as well. Furthermore, the proposed controller is extended to multi-agent systems under iteration-varying graph. It turns out that the developed controller is very robust to communication variations. In the numerical study, three illustrative examples are presented to show the effectiveness of the proposed controller. The learning controller with input sharing demonstrates not only faster convergence but also smooth transient performance.     

On iterative learning control design for tracking iteration-varying trajectories with high-order internal model

In this paper, iterative learning control (ILC) design is studied for an iteration-varying tracking problem in which reference trajectories are generated by high-order internal models (HOIM). An HOIM formulated as a polynomial operator between consecutive iterations describes the changes of desired trajectories in the iteration domain and makes the iterative learning problem become iteration varying. The classical ILC for tracking iteration-invariant reference trajectories, on the other hand, is a special case of HOIM where the polynomial renders to a unity coefficient or a special first-order internal model. By inserting the HOIM into P-type ILC, the tracking performance along the iteration axis is investigated for a class of continuous-time nonlinear systems. Time-weighted norm method is utilized to guarantee validity of proposed algorithm in a sense of data-driven control.     

Varying trail lengths-based iterative learning control for linear discrete-time systems with vector relative degree

In this article, to tackle with the iteration-varying trail lengths and random initial state shifts, an average operator-based PD-type iterative learning control (ILC) law is firstly presented for linear discrete-time multiple-input multiple-output (MIMO) systems with vector relative degree. The proposed PD-type ILC law includes an initial rectifying action against initial state shifts, and pursues the reference trajectory tracking beyond the initial time points. As special cases of the PD-type ILC law, P-type and D-type ILC laws are then introduced. It is proved that for linear discrete-time MIMO systems with vector relative degree, the three proposed ILC laws can drive the varying trail lengths-based ILC tracking errors to zero in mathematical expectation beyond the initial time points. A numerical example is used to illustrate the effectiveness of the proposed ILC laws.     

Adaptive ILC for a class of discrete-time systems with iteration-varying trajectory and random initial condition

In this work we present a discrete-time adaptive iterative learning control (AILC) scheme to deal with systems with time-varying parametric uncertainties. Using the analogy between the discrete-time axis and the iterative learning axis, the new adaptive ILC can incorporate a Recursive Least Squares (RLS) algorithm, hence the learning gain can be tuned iteratively along the learning axis and pointwisely along the time axis. When the initial states are random and the reference trajectory is iteration-varying, the new AILC can achieve the pointwise convergence over a finite time interval asymptotically along the iterative learning axis.