The advent of H -control was a truly remarkable innovation in multivariable theory. It eliminated the classical/modern dichotomy that had been a major source of the long-standing skepticism about the applicability of modern control theory, by amalgamating the "philosophy" of classical design with "computation" based on the state-space problem setting. It enhanced the application by deepening the theory mathematically and logically, not by weakening it as was done by the reformers of modern control theory in the early 1970s.

The purpose of this book is to provide a natural theoretical framework that is understandable with little mathematical background. The notion of chain-scattering, well known in classical circuit theory, but new to control theorists, plays a fundamental role in this book. It captures an essential feature of the control systems design, reducing it to a J-lossless factorization, which leads naturally to the idea of H-infinity-control. The J-lossless conjugation, an essentially new notion in linear system theory, then provides a powerful tool for computing this factorization. Thus the chain-scattering representation, the J-lossless factorization, and the J-lossless conjugation are the three key notions that provide the thread of development in this book. The book is completely self contained and requires little mathematical background other than some familiarity with linear algebra. It will be useful to applied mathematicians andpracticing engineers in control system design and as a text for a graduate course in H -control and its applications. "

Through its rapid progress in the last decade, HOOcontrol became an established control technology to achieve desirable performances of con trol systems. Several highly developed software packages are now avail able to easily compute an HOOcontroller for anybody who wishes to use HOOcontrol. It is questionable, however, that theoretical implications of HOOcontrol are well understood by the majority of its users. It is true that HOOcontrol theory is harder to learn due to its intrinsic mathemat ical nature, and it may not be necessary for those who simply want to apply it to understand the whole body of the theory. In general, how ever, the more we understand the theory, the better we can use it. It is at least helpful for selecting the design options in reasonable ways to know the theoretical core of HOOcontrol. The question arises: What is the theoretical core of HOO control? I wonder whether the majority of control theorists can answer this ques tion with confidence. Some theorists may say that the interpolation theory is the true essence of HOOcontrol, whereas others may assert that unitary dilation is the fundamental underlying idea of HOOcontrol. The J spectral factorization is also well known as a framework of HOOcontrol. A substantial number of researchers may take differential game as the most salient feature of HOOcontrol, and others may assert that the Bounded Real Lemma is the most fundamental building block."

This volume is composed of invited papers on learning and control. The contents form the proceedings of a workshop held in January 2008, in Hyderabad, that honoured the 60th birthday of Doctor Mathukumalli Vidyasagar.

The 14 papers, written by international specialists in the field, cover a variety of interests within the broader field of learning and control. The editors have grouped these into the following 3 categories:

a [ learning and computational issues

a [ learing for communication and identification

a [ applications of learning and control

The diversity of the research presented gives the reader a unique opportunity to explore a comprehensive overview of a field of great interest to control and system theorists. Specific topics include: a look at progress toward a unified view of communication and control; a new type of neural computation; a review of 50 years of the Pontryagin maximum principle; the control of smart materials and the uses of monotone systems in systems biology.

The reader will benefit from the expert participantsa (TM) ideas on the exciting new approaches to control and system theory and their predictions of future directions for the subject that were discussed at the workshop.