- ISBN:9787506282949
- 装帧:一般胶版纸
- 册数:暂无
- 重量:暂无
- 开本:24开
- 页数:667 页
- 出版时间:2007-05-01
- 条形码:9787506282949 ; 978-7-5062-8294-9
本书特色
非线性系统的研究近年来受到越来越广泛的关注,国外许多工科院校已将“非线性系统”作为相关专业研究生的学位课程。本书介绍了非线性系统的基本概念和基本分析方法;输入-输出稳定性、无源性和反馈系统的频域分析;现代稳定性分析的基本概念、扰动系统的稳定性、扰动理论和平均化以及奇异扰动理论;反馈控制的基本概念的反馈线性化,并给出了几种非线性设计工具,如滑模控制、Lyapunov再设计、反步法、基于无源的控制和高增益观测器等。此外本书附录还汇集了一些书中用到的数学知识,包括基本数学知识的复习、压缩映射和一些较为复杂的定理证明。 本书既可以作为研究生**学期非线性系统课程的教材,也可以作为工程技术人员、应用数学专业人员的自学教材或参考书。
内容简介
近十年来非线性系统中分析与控制出现了许多新的数学工具,几何非线性控制的综合理论也有较大发展,基于此,非线性系统模拟和精密实时非线性控制律的计算功能有了巨大的进步。这种技巧上的发展促进了分析方法的发展。本书简要介绍了分析的方法和工具。
目录
Acknowledgments
Standard Notation
1 Linear vs. Nonlinear
1.1 Nonlinear Models
1.2 Complexity in Nonlinear Dynamics
1.2.1 Subtleties of Nonlinear Systems Analysis
1.2.2 Autonomous Systems and Equilibrium Points
1.3 Some Classical Examples
1.3.1 The Tunnel Diode Circuit
1.3.2 An Oscillating Circuit: Due to van der Po!
1.3.3 The Pendulum: Due to Newton
1.3.4 The Buckling Beam: Due to Euler
1.3.5 The Volterra-Lotka Predator-Prey Equations
1.4 Other Classics: Musical Instruments
1.4.1 Blowing of a Clarinet Reed: Due to Rayleigh
1.4.2 Bowing of a Violin String: Due to Rayleigh
1.5 Summary
1.6 Exercises
2 Planar Dynamical Systems
2.1 Introduction
2.2 Linearization About Equilibria of Second-Order Nonlinear Systems
2.2.1 Linear Systems in the Plane
2.2.2 Phase Portraits near Hyperbolic Equilibria
2.3 Closed Orbits of Planar Dynamical Systems
2.4 Counting Equilibria: Index Theory
2.5 Bifurcations
2.6 Bifurcation Study of Josephson Junction Equations
2.7 The Degenerate van der Pol Equation
2.8 Planar Discrete-Time Systems
2.8.1 Fixed Points and the Hartman-Grobman Theorem
2.8.2 Period N Points of Maps
2.8.3 Bifurcations of Maps
2.9 Summary
2.10 Exercises
3 Mathematical Background
3.1 Groups and Fields
3.2 Vector Spaces, Algebras, Norms, and Induced Norms
3.3 Contraction Mapping Theorems
3.3.1 Incremental Small Gain Theorem
3.4 Existence and Uniqueness Theorems for Ordinary Differential Equations
3.4.1 Dependence on Initial Conditions on Infinite Time Intervals
3.4.2 Circuit Simulation by Waveform Relaxation
3.5 Differential Equations with Discontinuities
3.6 Carleman Linearization
3.7 Degree Theory
3.8 Degree Theory and Solutions of Resistive Networks
3.9 Basics of Differential Topology
3.9.1 Smooth Manifolds and Smooth Maps
3.9.2 Tangent Spaces and Derivatives
3.9.3 Regular Values
3.9.4 Manifolds with Boundary
3.10 Summary
3.11 Exercises
4 Input-Output Analysis
4.1 Optimal Linear Approximants to Nonlinear Systems
4.1.1 Optimal Linear Approximations for Memoryless, Time-Invariant Nonlinearities
4.1.2 Optimal Linear Approximations for Dynamic Nonlinearities: Oscillations in Feedback Loops
4.1.3 Justification of the Describing Function
4.2 Input-Output Stability.
4.3 Applications of the Small Gain Theorems
……
5 Lyapunov Stability THeory
6 Applications of Lyapunov THeory
7 Dynamical Systems and Bifurcations
8 Basics of Differential Geometry
9 Linearization by State Feedback
10 Design Examples Using Linearization
11 Geometric Nonlinear Control
12 Exterior Differential Systems in Control
13 New Vistas: Multi-Agent Hybrid Systems
References
Index
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