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. Contents......Page 11 Part I: Methodology......Page 15 1. Preliminaries......Page 16 1.1 Analytic and Meromorphic Functions......Page 17 1.2 Control Systems......Page 21 1.3 Linear Algebraic Setting......Page 23 1.4 Frobenius Theorem......Page 27 1.5 Examples......Page 29 Problems......Page 31 2.1 State Elimination......Page 33 2.2 Examples......Page 37 2.3 Generalized Realization......Page 38 2.4 Classical Realization......Page 40 2.5 Input-output Equivalence and Realizations......Page 41 2.6 A Necessary and Sufficient Condition for the Existence of a Realization......Page 43 2.7 Minimal Realizations......Page 45 2.8 Affine Realizations......Page 46 2.9 The Hopping Robot......Page 51 2.10 Some Models......Page 53 Problems......Page 54 3.2 Examples......Page 56 3.3 Reachability, Controllability, and Accessibility......Page 57 3.4 Autonomous Elements......Page 58 3.5 Accessible Systems......Page 60 3.6 Controllability Canonical Form......Page 61 3.7 Controllability Indices......Page 62 Problems......Page 64 4.2 Examples......Page 66 4.3 Observability......Page 67 4.4 The Observable Space......Page 68 4.5 Observability Canonical Form......Page 71 4.6 Observability Indices......Page 72 4.7 Synthesis of Observers......Page 73 Problems......Page 80 5.1 Introductory Examples......Page 81 5.2 Inverse Systems......Page 82 5.3 Structural Indices......Page 83 5.4 Structure Algorithm......Page 86 5.5 Invertibility......Page 93 5.6 Zero Dynamics......Page 94 Problems......Page 97 6.1 Generalized State-space Transformation......Page 99 6.2 Regular Generalized State Feedback......Page 100 6.3 Generalized Output Injection......Page 102 6.4 Canonical Form......Page 103 6.5 Generalizing the Notion of Output Injection......Page 109 Problem......Page 112 Part II: Applications to Control Problems......Page 113 7.1 Input-output Linearization Problem Statement......Page 114 7.3 Multioutput Case......Page 115 7.4 Trajectory Tracking......Page 118 Problems......Page 122 8.1 Noninteracting Control Problem Statement......Page 123 8.3 Dynamic State Feedback Solution......Page 124 8.4 Noninteracting Control via Quasi-static State Feedback......Page 125 Problem......Page 126 9.1 Input-state Linearization Problem Statement......Page 127 9.2 Static State Feedback Solution......Page 128 9.3 Partial Linearization......Page 130 Problem......Page 134 10. Disturbance Decoupling......Page 135 10.1 Solution of the Disturbance Decoupling Problem......Page 136 11.1 A Special Form of the Inversion Algorithm......Page 138 11.2 Model Matching Problem......Page 141 11.3 Left Factorization......Page 149 12.1 Input-output Linearization......Page 156 12.2 Input-output Decoupling......Page 171 Problem......Page 172 C......Page 173 D......Page 174 F......Page 175 H......Page 176 J......Page 177 M......Page 178 R......Page 179 Z......Page 180 O......Page 182 Z......Page 183 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.