The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Editor-in-Chief Jurgen Appell, Wurzburg, Germany Honorary and Advisory Editors Catherine Bandle, Basel, Switzerland Alain Bensoussan, Richardson, Texas, USA Avner Friedman, Columbus, Ohio, USA Umberto Mosco, Worcester, Massachusetts, USA Louis Nirenberg, New York, USA Alfonso Vignoli, Rome, Italy Editorial Board Manuel del Pino, Bath, UK, and Santiago, Chile Mikio Kato, Nagano, Japan Wojciech Kryszewski, Torun, Poland Vicentiu D. Radulescu, Krakow, Poland Simeon Reich, Haifa, Israel Please submit book proposals to Jurgen Appell. Titles in planning include Lucio Damascelli and Filomena Pacella, Morse Index of Solutions of Nonlinear Elliptic Equations (2019) Tomasz W. Dlotko and Yejuan Wang, Critical Parabolic-Type Problems (2019) Rafael Ortega, Periodic Differential Equations in the Plane: A Topological Perspective (2019) Ireneo Peral Alonso and Fernando Soria, Elliptic and Parabolic Equations Involving the Hardy-Leray Potential (2020) Cyril Tintarev, Profile Decompositions and Cocompactness: Functional-Analytic Theory of Concentration Compactness (2020) Takashi Suzuki, Semilinear Elliptic Equations: Classical and Modern Theories (2021)

This book describes the evolution of feedback theory, from its simplest form to more complex guises, and connects this to the control of complex systems. It systematically develops a new approach to the synthesis of non-linear feedback controllers under uncertainty. This book aims to increase the understanding of potential reactions of such systems to uncertain forces and unknown factors contained in feedback mechanisms. The theoretical basis for a new generation of perfect automatic systems is introduced.

This book is written for the wide circle of readers who take an interest in concepts of basic sciences, specifically cybernetics, automation and control. It aims to provide a new technique for the solution of a range of automatic control problems using n ew types of feedback loops. Simple examples are used to illustrate the basic problems, the important aspects of the theory of automatic control and the difficulties that have to be faced when considering the automation of actual objects. Control of Indefinite Nonlinear Dynamic Systems is the first book to set out an effective regular procedure for the synthesis of robust feedback loops. This signifies an advancement in the area of general feedback which deal with problems of robust contro l under conditions of uncertainty.