An algorithm for Iterative Learning Control is proposed based on an optimization principle used by other authors to derive gradient type algorithms. The new algorithm is a descent algorithm and has potential benefits which include realization in terms of Riccati feedback and feedforward components. This realization also has the advantage of implicitly ensuring automatic step size selection and hence guaranteeing convergence without the need for empirical choice of parameters. The algorithm achieves a geometric rate of convergence for invertible plants. One important feature of the proposed algorithm is the dependence of the speed of convergence on weight parameters appearing in the norms of the signals chosen for the optimization problem.

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SUMMARYThis paper considers the use of matrix models and the robustness of a gradient-based iterative learning control (ILC) algorithm using both fixed learning gains and nonlinear data-dependent gains derived from parameter optimization. The philosophy of the paper is to ensure monotonic convergence with respect to the mean-square value of the error time series. The paper provides a complete and rigorous analysis for the systematic use of the well-known matrix models in ILC. Matrix models provide necessary and sufficient conditions for robust monotonic convergence. They also permit the construction of accurate sufficient frequency domain conditions for robust monotonic convergence on finite time intervals for both causal and non-causal controller dynamics. The results are compared with recently published results for robust inverse-model-based ILC algorithms and it is seen that the algorithm has the potential to improve the robustness to high-frequency modelling errors, provided that resonances within the plant bandwidth have been suppressed by feedback or series compensation.

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This paper considers the robustness of an inverse iterative learning control algorithm. A simple learning gain results in robust convergence that is monotonic in the least squares sense provided that the multiplicative plant uncertainty satisfies a matrix positivity requirement. The results are extended to the frequency domain using a simple graphical Nyquist test. The analysis extends naturally to a parameter-optimal control setting. Non-monotone convergence is considered by using a simple weighted norm based on exponential weighting of time series.

Abstract-Discrete linear repetitive processes are a distinct class of two-dimensional (2-D) linear systems with applications in areas ranging from long-wall coal cutting through to iterative learning control schemes. The feature which makes them distinct from other classes of 2-D linear systems is that information propagation in one of the two distinct directions only occurs over a finite duration. This, in turn, means that a distinct systems theory must be developed for them. In this paper, an LMI approach is used to produce highly significant new results on the stability analysis of these processes and the design of control schemes for them. These results are, in the main, for processes with singular dynamics and for those with so-called dynamic boundary conditions. Unlike other classes of 2-D linear systems, these feedback control laws have a firm physical basis, and the LMI setting is also shown to provide a (potentially) very powerful setting in which to characterize the robustness properties of these processes.