非線性控制系統(tǒng)的分析與設(shè)計

前言

　　The purpose of this book is to present a comprehensive introduction to the theoryand design technique of nonlinear control systems. It may serve as a standard refer-ence of nonlinear control theory and applications for control scientists and controlengineers as well as Ph.D students majoring in Automation or some related fieldssuch as Operational Research， Management， Communication etc.　 In the book we emphasize on the geometric approach to nonlinear control systems. In fact， we intend to put nonlinear control theory and its design techniquesinto a geometric framework as much as we can. The main motivation to write thisbook is to bring readers with basic engineering background promptly to the frontier of the modem geometric approach on the dynamic systems， particularly on theanalysis and control design of nonlinear systems.　 We have made a considerable effort on the following aspects：　 First of all， we try to visualize the concepts. Certain concepts are defined overlocal coordinates， but in a coordinate free style. The purpose for this is to makethem easily understandable， particularly at the first reading. Through this way areader can understand a concept by just considering the case in n. Later on， whenthe material has been digested， it is easy to lift them to general topological spacesor manifolds.　 Secondly， we emphasize the numerical or computational aspect. We believe thatmaking things computable is very useful not only for solving engineering problemsbut also for understanding the concepts and methods.　 Thirdly， certain proofs have been simplified and some elementary proofs are pre-sented to make the materials more readable for engineers or readers not specializingin mathematics. Finally， the topics which can be found easily in some other standardtextbooks or references are briefly introduced and the corresponding references areincluded. Much attention has been put on new topics， new results， and new designtechniques.　 For convenience， a brief survey on linear control theory is included， which canbe skipped for readers who are already familiar with the subject. For those whoare not majoring in control theory， it provides a tutorial introduction to the field，which is sufficient for the further study of this book. The other mathematical pre-requirements are Calculus， Linear Algebra， Ordinal Differential Equation.

內(nèi)容概要

本書全面介紹了非線性控制系統(tǒng)的分析與設(shè)計。全書共分為兩部分。其中第一部分為第1～4章。第1章介紹了拓撲空間，第2章介紹了微流形，第3章介紹了代數(shù)、Lie群和Lie代數(shù)，它們?yōu)楸緯峁┝搜芯繑?shù)學背景。第二部分包括12章，即第5～16章，這些章節(jié)涵蓋了可控性、可觀測性、穩(wěn)定性、解耦、投入產(chǎn)出的實現(xiàn)、線性化、中心流技術(shù)、輸出調(diào)節(jié)、耗散系統(tǒng)、H∞控制、切換系統(tǒng)和非平穩(wěn)控制等方面，并給出了有關(guān)的詳細設(shè)計技術(shù)。 本書可供理工科大學自動控制專業(yè)的教師及研究生閱讀，也可供自然科學和工程技術(shù)領(lǐng)域中相關(guān)專業(yè)的研究人員參考。

作者簡介

　　Dr. Daizhan Cheng， a professor at Institute of Systems Science， Chinese Academy of Sciences， has been working on the control of nonlinear systems for over 30 years and is currently a Fellow of IEEE and a Fellow of IFAC， he is also the chairman of Technical Committee on Control Theory， Chinese Association of Automation.

書籍目錄

1.  Introduction  1.1  Linear Control Systems    1.1.1  Controllability, Observability    1.1.2  Invariant Subspaces    1.1.3  Zeros, Poles, Observers    1.1.4  Normal Form and Zero Dynamics  1.2  Nonlinearity vs Linearity    1.2.1  Localization    1.2.2  Singularity    1.2.3  Complex Behaviors  1.3  Some Examples of Nonlinear Control Systems  References2.  Topological Space  2.1  Metric Space  2.2  Topological Spaces  2.3  Continuous Mapping  2.4  Quotient Spaces  References3.  Differentiab!e Manifold  3.1  Structure of Manifolds  3.2  Fiber Bundle  3.3  Vector Field  3.4  One Parameter Group  3.5  Lie Algebra of Vector Fields  3.6  Co-tangent Space  3.7  Lie Derivatives  3.8  Frobenius' Theory  3.9  Lie Series, Chow's Theorem  3.10  Tensor Field  3.11  Riemannian Geometry  3.12  Symplectic Geometry  References4.  Algebra, Lie Group and Lie Algebra  4.1  Group  4.2  Ring and Algebra  4.3  Homotopy  4.4  Fundamental Group  4.5  Covering Space  4.6  Lie Group  4.7  Lie Algebra of Lie Group  4.8  Structure of Lie Algebra  References5.  Controllability and Observability  5.1  Controllability of Nonlinear Systems  5.2  Observability of Nonlinear Systems  5.3  Kalman Decomposition  References6.  Global Controllability of Affine Control Systems  6.1  From Linear to Nonlinear Systems  6.2  A Sufficient Condition  6.3  Multi-hierarchy Case  6.4  Codim = 1  References7.  Stability and Stabilization  7.1  Stability of Dynamic Systems  7.2  Stability in the Linear Approximation  7.3  The Direct Method of Lyapunov    7.3.1  Positive Definite Functions    7.3.2  Critical Stability    7.3.3  Instability    7.3.4  Asymptotic Stability    7.3.5  Total Stability    7.3.6  Global Stability  7.4  LaSalle's Invariance Principle  7.5  Converse Theorems to Lyapunov's Stability Theorems    7.5.1  Converse Theorems to Local Asymptotic Stability    7.5.2  Converse Theorem to Global Asymptotic Stability  7.6  Stability of Invariant Set  7.7  Input-Output Stability    7.7.1  Stability of Input-Output Mapping    7.7.2  The Lur'e Problem    7.7.3  Control Lyapunov Function  7.8  Region of Attraction  References8.  Deeoupling  8.1  (f,g)-invariant Distribution  8.2  Local Disturbance Decoupling  8.3  Controlled Invariant Distribution  8.4  Block Decomposition  8.5  Feedback Decomposition  References9.  Input-Output Structure  9.1  Decoupling Matrix  9.2  Morgan's Problem  9.3  Invertibility  9.4  Decoupling via Dynamic Feedback  9.5  Normal Form of Nonlinear Control Systems  9.6  Generalized Normal Form  9.7  Fliess Functional Expansion  9.8  Tracking via Fliess Functional Expansion    References10. Linearization of Nonlinear Systems  10.1  Poincare Linearization  10.2  Linear Equivalence of Nonlinear Systems  10.3  State Feedback Linearization  10.4  Linearization with Outputs  10.5  Global Linearization  10.6  Non-regular Feedback Linearization  References11 Design of Center Manifold  11.1  Center Manifold  11.2  Stabilization of Minimum Phase Systems  11.3  Lyapunov Function with Homogeneous Derivative  11.4  Stabilization of Systems with Zero Center  11.5  Stabilization of Systems with Oscillatory Center  11.6  Stabilization Using Generalized Normal Form  11.7  Advanced Design Techniques  References12 Output Regulation  12.1  Output Regulation of Linear Systems  12.2  Nonlinear Local Output Regulation  12.3  Robust Local Output Regulation  References13 Dissipative Systems  13.1  Dissipative Systems  13.2  Passivity Conditions  13.3  Passivity-based Control  13.4  Lagrange Systems  13.5  Hamiltonian Systems  References14 L2-Gain Synthesis  14.1  H∞ Norm and//2-Gain  14.2  H∞ Feedback Control Problem  14.3  L2-Gain Feedback Synthesis  14.4  Constructive Design Method  14.5  Applications  References15 Switched Systems  15.1  Common Quadratic Lyapunov Function  15.2  Quadratic Stabilization of Planar Switched Systems  15.3  Controllability of Switched Linear Systems  15.4  Controllability of Switched Bilinear Systems  15.5  LaSalle's Invariance Principle for Switched Systems  15.6 Consensus of Multi-Agent Systems    15.6.1  Two Dimensional Agent Model with a Leader    15.6.2  n Dimensional Agent Model without Lead  References16 Discontinuous Dynamical Systems  16.1  Introduction  16.2  Filippov Framework    16.2.1  Filippov Solution    16.2.2  Lyapunov Stability Criteria  16.3  Feedback Stabilization    16.3.1  Feedback Controller Design: Nominal Case    16.3.2  Robust Stabilization  16.4  Design Example of Mechanical Systems    16.4.1  PD Controlled Mechanical Systems    16.4.2  Stationary Set    16.4.3  Application Example  ReferencesAppendix A  Some Useful Theorems  A.1  Sard's Theorem  A.2  Rank Theorem  ReferencesAppendix B  Semi-Tensor Product of Matrices  B.1  A Generalized Matrix Product  B.2  Swap Matrix  B.3  Some Properties of Semi-Tensor Product  B.4  Matrix Form of Polynomials  ReferencesIndex

編輯推薦

　　Analysis and Design of Nonlinear Control Systems provides a comprehensive and up to date introduction to nonlinear control systems， including system analysis and major control design techniques. The book is self-contained， providing sufficient mathematical foundations for understanding the contents of each chapter. Scientists and engineers engaged in the field of Nonlinear Control Systems will find it an extremely useful handy reference book.

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