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The problem of iterative learning control (ILC) is considered for a class of time-varying systems with random packet dropouts. It is assumed that an ILC scheme is implemented via a remote control system and that packet dropout occurs during the packet transmission between the ILC controller and the actuator of remote plant. The packet dropout is viewed as a binary switching sequence which is subject to the Bernoulli distribution. In order to eliminate the effect of packet dropouts on the convergence property of output error, the hold-input scheme is adopted to compensate the packet dropout at the actuator. It is shown that the hold-input scheme with average ILC can achieve asymptotical convergence along the iteration axis for discrete time-varying linear system. Numerical examples are provided to show the effectiveness of the proposed method.

Iterative learning control (ILC) is an attractive technique when dealing with systems that execute the same task repeatedly over a finite time interval [

On the other hand, the remote control systems have been the focus of several research studies over the last few years [

Besides the stability issue, trajectory tracking is a challenging issue for remote control systems. Fortunately, for periodic systems, iterative learning control offers a systematic design that can improve the tracking performance by iterations in a fixed time interval. ILC is in principle a feedforward technique; thus it can send the controller signals obtained from previous trials. It is still an open research area in ILC which is implemented via a remote systems setting, except for certain pioneer works [

In this paper, we proposed an ILC for a time-varying system with random packet dropouts. As depicted in previous studies [

The paper is organized as follows. Section

Consider the ILC system with network communication depicted in Figure

The schematic diagram of the networked control system.

At each

Given an output reference trajectory

The purpose of this paper is to design an iterative learning control law for the above plant with network communication such that

Denote

Expanding expression (

From (

Taking expectation on both sides of (

For any

For all

From (

For the system with network communication described in Section

From definition of average operator, note the relation

Applying the ensemble operator

Now let us handle the third term on the right hand side of (

Next, combining analogous terms on the right hand of (

Taking

Using Lemma

Combining Lemma

According to the relationship (

Similar to the proof of Lemma

Finally, from (

This completes the proof.

In this paper, we consider D-type iterative learning control with average operator, and the result obtained can be extended to P-type iterative learning control with average operator.

In this simulation test, let us consider system (

For expected value

As shown in Figure

The max tracking error versus iteration with 5% packet dropout.

The mathematical expectation of the tracking error versus iteration with 5% packet dropout.

In this work we address a remote control system problem with random packet dropout in controller-actuator channel. The hold-input scheme with average ILC is applied to handle this remote control problem with repeated tracking tasks. Through analysis we illustrate the desired convergence property of the hold-input scheme with average ILC. In our future work, we will also explore the extension to more generic stochastic process such as Markov chain.

The set of all real numbers

The set of all positive integers

The average operator

The expected value of a random variable

The probability of an event

The maximal singular value of a matrix

The Euclidean norm of a vector

Identity matrix of appropriate dimensions

Zero matrix of appropriate dimensions.

This work is supported by the 973 program of China (Grant no. 2009CB320603).