Limiting Behaviour in Parameter Optimal Iterative Learning Control

This paper analyses the concept of LIMIT SET in Iterative Learning Control. The authors investigate the existence of STABLE and UNSTABLE parts of the Limit Set and demonstrate that there will often exist in practice. This illustrated via a 2-dimensional example where the convergence of the learning algorithm is analysed from the error's dynamical behaviour. These ideas are extended to N-dimensional cases by analogy and example

Robust monotone gradient-based discrete-time iterative learning control

This 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.<br/