Algebraic Methods for Nonlinear Control Systems (Communications and Control Engineering)

A self-contained introduction to algebraic control for nonlinear systems suitable for researchers and graduate students. The most popular treatment of control for nonlinear systems is from the viewpoint of differential geometry yet this approach proves not to be the most natural when considering problems like dynamic feedback and realization. Professors Conte, Moog and Perdon develop an alternative linear-algebraic strategy based on the use of vector spaces over suitable fields of nonlinear functions. This algebraic perspective is complementary to, and parallel in concept with, its more celebrated differential-geometric counterpart. Algebraic Methods for Nonlinear Control Systems describes a wide range of results, some of which can be derived using differential geometry but many of which cannot. They include: • classical and generalized realization in the nonlinear context; • accessibility and observability recast within the linear-algebraic setting; • discussion and solution of basic feedback problems like input-to-output linearization, input-to-state linearization, non-interacting control and disturbance decoupling; • results for dynamic and static state and output feedback. Dynamic feedback and realization are shown to be dealt with and solved much more easily within the algebraic framework. Originally published as Nonlinear Control Systems, 1-85233-151-8, this second edition has been completely revised with new text – chapters on modeling and systems structure are expanded and that on output feedback added de novo – examples and exercises. The book is divided into two parts: the first being devoted to the necessary methodology and the second to an exposition of applications to control problems. This book provides a unique and alternative approach to the study of nonlinear control systems, with applications. The approach presented is based on the use of algebraic methods which are intrinsically linear, rather than differential geometric methods, which are more commonly found in other reference works on the subject. This allows the exposition to remain simple from a mathematical point of view, and accessible for everyone who has a good understanding of linear control theory. The book is divided into the following three parts: Part 1 is devoted to mathematical preliminaries and to the development of tools and methods for system analysis. Part 2 is concerned with solving specific control problems, including disturbance decoupling, non-interactive control, model matching and feedback linearization problems. Part 3 introduces differential algebraic notions and discusses their applications to nonlinear control and system theory. With numerous examples used to illustrate theoretical results, this self-contained and comprehensive volume will be of interest to all those who have a good basic knowledge of standard linear control systems A self-contained introduction to algebraic control for nonlinear systems suitable for researchers and graduate students.'Algebraic Methods for Nonlinear Control Systems'develops a linear-algebraic alternative to the usual differential-geometric approach to nonlinear control, using vector spaces over suitable fields of nonlinear functions. It describes a range of results, some of which can be derived using differential geometry but many of which cannot. They include: classical and generalized realization in the nonlinear context; accessibility and observability recast for the linear-algebraic setting; discussion and solution of basic feedback problems; results for dynamic and static state and output feedback. Dynamic feedback and realization are shown to be dealt with and solved much more easily in the algebraic framework. The second edition has been completely revised with new text, examples and exercises; it is divided into two parts: necessary methodology and applications to control problems. "The most popular treatment of control for nonlinear systems is from the viewpoint of differential geometry yet this approach proves not to be the most natural when considering problems like dynamic feedback and realization. Professors Conte, Moog and Perdon develop an alternative linear-algebraic strategy based on the use of vector spaces over suitable fields of nonlinear functions. This algebraic perspective is complementary to, and parallel in concept with, its more celebrated differential-geometric counterpart."--Jacket This is a self-contained introduction to algebraic control for nonlinear systems suitable for researchers and graduate students. It is the first book dealing with the linear-algebraic approach to nonlinear control systems in such a detailed and extensive fashion. It provides a complementary approach to the more traditional differential geometry and deals more easily with several important characteristics of nonlinear systems. The approach presented here is based on algebraic methods which are intrinsically linear, rather than differential geometric methods. This allows the exposition to remain simple from a mathematical point of view, and accessible for those with an understanding of linear control theory. G. Conte, C.h. Moog, And A.m. Perdon. Includes Bibliographical References (p. [151]-164) And Index.