Linear and nonlinear iterative learning control
``Iterative Learning Control'' (ILC) is a design technique which was first divised by S. Arimoto and colleagues about twenty years ago. The goal is to track exactly a given trajectory with suitable controls. The setting is that an experiment is repeated after a given interval of time has elapsed. There is a law which gives the value of the new control from the preceding one (depending on the error of the tracked profiles). This is where learning occurs. The initial conditions are always the same at the start of each iteration, but the control construction depends a priori on it so that it is not allowed to speak of feedback without detailed analysis. After an introductory section (idea of the method, history of the discipline, outline of the book), the situation using a contraction mapping theorem is presented. A global Lipschitz condition on the plant is assumed. The authors explore issues of convergence and try to determine if memory of more than one iteration is needed. The MIMO and nonlinear cases are studied in succession. A second part considers the more general situation of a local Lipschitz condition as an hypothesis on the plant. A ``composite energy function'' is used. The idea is to decompose the control into a stabilizing feedback and a learning control. The authors make connections with optimal control theory and a last chapter uses wavelets in this context. A conclusion points out open areas of research: further study of convergence issues when using the ``composite energy function'' method (which performs worse than the contraction mapping method), the discrete case, observation problems, analytic solutions, and the use of other learning methods (normal nets, statistical learning, etc.\dots). There are 153 references and an index. A chapter relating ILC and 2-D systems theory would have been welcome. The book will be of interest for teaching and learning ``iterative learning control''.
scientific article; zbMATH DE number 1952028