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Iterative learning control. Robustness and monotonic convergence for interval systems. (English) Zbl 1162.93025
Communications and Control Engineering. London: Springer (ISBN 978-1-84628-846-3/hbk). xviii, 230 p. (2007).
This monograph is an overview of results on iterative learning control of discrete time systems, wherein the controller ‘learns’ the control using error feedback through repeated operation of the system. It also includes some novel developments. It begins with a motivation, overview and literature survey, and then introduces the supervector framework for establishing conditions of asymptotic stability and monotone convergence of error (in a sense defined therein) for higher order systems. These results are followed by an extension to first order systems with interval uncertainty for parameters, to computation of maximal allowable uncertainty for asymptotic stability and monotone convergence, an alternative learning scheme when interval boundaries of parameter uncertainty are known, learning control for iteration domain uncertainty in the $$H_{\infty}$$ framework, and finally to stochastic systems, which also involves an appropriate extension of Kalman filtering. Concrete computational evidence is provided throughout. In the process of providing analytic techniques for iterated learning control, the monograph also derives come novel results for interval-based mathematics.

##### MSC:
 93C40 Adaptive control/observation systems 93E35 Stochastic learning and adaptive control 93C55 Discrete-time control/observation systems 93C35 Multivariable systems, multidimensional control systems
##### Software:
Polynomial Toolbox; INTLAB