Relaxing Fundamental Assumptions in Iterative Learning Control

Iterative learning control (ILC) is perhaps best decribed as an open loop feedforward control technique where the feedforward signal is learned through repetition of a single task. As the name suggests, given a dynamic system operating on a finite time horizon with the same desired trajectory, ILC aims to iteratively construct the inverse image (or its approximation) of the desired trajectory to improve transient tracking. In the literature, ILC is often interpreted as feedback control in the iteration domain due to the fact that learning controllers use information from past trials to drive the tracking error towards zero. However, despite the significant body of literature and powerful features, ILC is yet to reach widespread adoption by the control community, due to several assumptions that restrict its generality when compared to feedback control. In this dissertation, we relax some of these assumptions, mainly the fundamental invariance assumption, and move from the idea of learning through repetition to two dimensional systems, specifically repetitive processes, that appear in the modeling of engineering applications such as additive manufacturing, and sketch out future research directions for increased practicality: We develop an L1 adaptive feedback control based ILC architecture for increased robustness, fast convergence, and high performance under time varying uncertainties and disturbances. Simulation studies of the behavior of this combined L1-ILC scheme under iteration varying uncertainties lead us to the robust stability analysis of iteration varying systems, where we show that these systems are guaranteed to be stable when the ILC update laws are designed to be robust, which can be done using existing methods from the literature. As a next step to the signal space approach adopted in the analysis of iteration varying systems, we shift the focus of our work to repetitive processes, and show that the exponential stability of a nonlinear repetitive system is equivalent to that of its linearization, and consequently uniform stability of the corresponding state space matrix.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133232/1/altin_1.pd

When is a parameterized controller suitable for adaptive control ?

International audienceIn this paper we investigate when a parameterized controller, designed for a plant depending on unknown parameters, admits a realization which is independent of the parameters. It is argued that adaptation is unnecessary for this class of parameterized controllers. We prove that standard model reference controllers (state and output--feedback) for linear time invariant systems with a filter at the plant input admit a parameter independent realization. Although the addition of such a filter is of questionable interest, our result formally, and unquestionably, establishes the deleterious effect of such a modification, which has been widely publicized in the control literature under the name L1-adaptive control

A stability-theory perspective to synchronisation of heterogeneous networks

Dans ce mémoire, nous faisons une présentation de nos recherches dans le domaine de la synchronisation des systèmes dynamiques interconnectés en réseau. Une des originalités de nos travaux est qu'ils portent sur les réseaux hétérogènes, c'est à dire, des systèmes à dynamiques diverses. Au centre du cadre d'analyse que nous proposons, nous introduisons le concept de dynamique émergente. Il s'agit d'une dynamique "moyennée'' propre au réseau lui-même. Sous l'hypothèse qu'il existe un attracteur pour cette dynamique, nous montrons que le problème de synchronisation se divise en deux problèmes duaux : la stabilité de l'attracteur et la convergence des trajectoires de chaque système vers celles générées par la dynamique émergente. Nous étudions aussi le cas particulier des oscillateurs de Stuart-Landau