Discrete-time model-based Iterative Learning Control: stability, monotonicity and robustness

In this thesis a new robustness analysis for model-based Iterative Learning Control (ILC) is presented. ILC is a method of control for systems that are required to track a reference signal in a repetitive manner. The repetitive nature of such a system allows for the use of past information such that the control system iteratively learns control signals that give high levels of tracking. ILC algorithms that learn in a monotonic fashion are desirable as it implies that tracking performance is improved at each iteration. A number of model-based ILC algorithms are known to result in a monotonically converging tracking error signal. However clear and meaningful robustness conditions for monotonic convergence in spite of model uncertainty are lacking. This thesis gives new robustness conditions for monotonically converging tracking error for two-model based ILC algorithms: the inverse and adjoint algorithms. It is found that the two algorithms can always guarantee robust monotone convergence to zero error if the multiplicative plant uncertainty matrix satisfies a matrix positivity requirement. This result is extended to the frequency domain using a simple graphical test. The analysis further extends to a Parameter Optimal control setting where optimisation is applied to the inverse and adjoint algorithms. The results show an increased degree in robust monotone convergence upon a previous attempt to apply optimisation to the two algorithms. This thesis further considers the case where the multiplicative plant uncertainty fails to satisfy the positivity requirement. Robustness analysis shows that use of an appropriately designed filter with the inverse or adjoint algorithm allows a filtered error signal to monotonically converge to zero.