Iterative learning control

Abstract: This article surveyed the major results in iterative learning control (ILC) analysis and design over the past two decades. Problems in stability, performance, learning transient behavior, and robustness were discussed along with four design techniques that have emerged as among the most popular. The content of this survey was selected to provide the reader with a broad perspective of the important ideas, potential, and limitations of ILC. Indeed, the maturing field of ILC includes many results and learning algorithms beyond the scope of this survey. Though beginning its third decade of active research, the field of ILC shows no sign of slowing down.

Abstract: In this paper we propose a new framework for learning from large scale datasets based on iterative learning from small mini-batches. By adding the right amount of noise to a standard stochastic gradient optimization algorithm we show that the iterates will converge to samples from the true posterior distribution as we anneal the stepsize. This seamless transition between optimization and Bayesian posterior sampling provides an inbuilt protection against overfitting. We also propose a practical method for Monte Carlo estimates of posterior statistics which monitors a "sampling threshold" and collects samples after it has been surpassed. We apply the method to three models: a mixture of Gaussians, logistic regression and ICA with natural gradients.

Abstract: A methodology is presented of feedback control to achieve accurate tracking for a class of nonlinear time-varying systems in the presence of disturbances and parameter variations. The methodology uses in its idealized form piecewise continuous feedback control laws, resulting in the state trajectory `sliding' along a discontinuity surface in the state space. The idealized form of the methodology results in perfect tracking of the required signals; however certain non-idealities associated with its implementation cause the trajectory to 'chatter' along the sliding surface resulting in the generation of an undesirable high-frequency component which may excite high-frequency unmodelled dynamics of the control systems. To rectify this situation, it is shown how continuous control laws which approximate the discontinuous control law may be used to obtain disturbance and parameter variation insensitive tracking. At the same time, the continuous control laws decrease the extent of unwanted high-frequency signals.

Abstract: In this paper, the iterative learning control (ILC) literature published between 1998 and 2004 is categorized and discussed, extending the earlier reviews presented by two of the authors. The papers includes a general introduction to ILC and a technical description of the methodology. The selected results are reviewed, and the ILC literature is categorized into subcategories within the broader division of application-focused and theory-focused results.