Iterative Learning Control

This monograph studies the design of robust, monotonically-convergent iterative learning controllers for discrete-time systems. Two key problems with the fundamentals of iterative learning control (ILC) design as treated by existing work are: first, many ILC design strategies assume nominal knowledge of the system to be controlled and; second, it is well-known that many ILC algorithms do not produce monotonic convergence, though in applications monotonic convergence is often essential. Iterative Learning Control takes account of the recently-developed comprehensive approach to robust ILC analysis and design established to handle the situation where the plant model is uncertain. Considering ILC in the iteration domain, it presents a unified analysis and design framework that enables designers to consider both robustness and monotonic convergence for typical uncertainty models, including parametric interval uncertainties, iteration-domain frequency uncertainty, and iteration-domain stochastic uncertainty. Topics include: • Use of a lifting technique to convert the two-dimensional ILC system, which has dynamics in both the time and iteration domains, into the supervector framework, which yields a one-dimensional system, with dynamics only in the iteration domain. • Development of iteration-domain uncertainty models in the supervector framework. • ILC design for monotonic convergence when the plant is subject to parametric interval uncertainty in its Markov matrix. • An algebraic H-infinity design methodology for ILC design when the plant is subject to iteration-domain frequency uncertainty. • Development of Kalman-filter-based ILC algorithms when the plant is subject to iteration-domain stochastic uncertainties. • Analytical determination of the base-line error of ILC algorithms. • Solutions to three fundamental robust interval computational problems (used as basic tools for designing robust ILC controllers): finding the maximum singular value of an interval...