Zhong-Ping Jiang - Trends in Nonlinear and Adaptive Control: A Tribute to Laurent Praly for his 65th Birthday

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This book is a tribute to

Laurent Praly

on the occasion of his 65th birthday. Throughout his 40 year career Laurent has contributed ground-breaking results, has initiated research directions, has laid the foundations of adaptive control, nonlinear stabilization, nonlinear observer design, and network systems, and has motivated, guided, and forged students, junior researchers, and colleagues. In addition, he has been a driving force for the intellectual and cultural growth of the systems and control community worldwide.

The volume collects nine contributions written by a total of seventeen researchers. The leading author of each contribution has been selected among the researchers who have worked or interacted with Laurent, have been influenced by his research activity, or have had the privilege and honor of being his Ph.D. students. The contributions focus on two foundational areas of control theory: nonlinear control and adaptive control, in which Laurent has been an undisputed top player for four decades. The diversity of the areas covered and the depth of the results are tangible evidence of Laurents impact on the way control problems are currently studied and results are developed. Control would be a very different discipline without Laurents vision and without his ability to push the boundaries of what is known and achievable. Laurents papers are timeless: the results therein are fundamental and are never superseded by more advanced or newer results. They constitute cornerstones upon which generations of control theorists will build. Similarly, practitioners and industrialists have greatly benefited from Laurents engineering ingenuity and tools.

As anticipated, the contributions in the book reflect important areas which have been pioneered and influenced by Dr. L. Praly, as detailed hereafter.

It has been known since a long time that invertible MIMO nonlinear systems can be input--output linearized via dynamic state feedback. However, the techniques originally developed to achieve this design goal are fragile, as they require the availability of an accurate model of the plant and access to the full state. Very recently, a robust version of these techniques has been developed, by means of which a linear input--output behavior can be approximated up to any arbitrarily fixed degree of accuracy. As a byproduct, for a strongly minimum phase invertible MIMO system, these techniques provide a robust stabilization paradigm, which can be also used in wider contexts, for instance, to simplify the solution of a problem of output regulation. The chapter , by A. Isidori and Y. Wu, reviews the techniques in question and their application to the design of output regulators.

The chapter , by A. Teel, considers using a differential inclusion, instead of a hybrid system, to effectuate a linear control system with resets. In particular, it establishes global exponential stability for the differential inclusion when the hybrid version of the reset control system admits a strongly convex Lyapunov function that establishes stability.