非线性系统

Preface

Acknowledgments

StandardNotation

1Linearvs.Nonlinear

1.1NonlinearModels

1.2ComplexityinNonlinearDynamics

1.2.1SubtletiesofNonlinearSystemsAnalysis

1.2.2AutonomousSystemsandEquilibriumPoints

1.3SomeClassicalExamples

1.3.1TheTunnelDiodeCircuit

1.3.2AnOscillatingCircuit:DuetovanderPo!

1.3.3ThePendulum:DuetoNewton

1.3.4TheBucklingBeam:DuetoEuler

1.3.5TheVolterra-LotkaPredator-PreyEquations

1.4OtherClassics:MusicalInstruments

1.4.1BlowingofaClarinetReed:DuetoRayleigh

1.4.2BowingofaViolinString:DuetoRayleigh

1.5Summary

1.6Exercises

2PlanarDynamicalSystems

2.1Introduction

2.2LinearizationAboutEquilibriaofSecond-OrderNonlinearSystems

2.2.1LinearSystemsinthePlane

2.2.2PhasePortraitsnearHyperbolicEquilibria

2.3ClosedOrbitsofPlanarDynamicalSystems

2.4CountingEquilibria:IndexTheory

2.5Bifurcations

2.6BifurcationStudyofJosephsonJunctionEquations

2.7TheDegeneratevanderPolEquation

2.8PlanarDiscrete-TimeSystems

2.8.1FixedPointsandtheHartman-GrobmanTheorem

2.8.2PeriodNPointsofMaps

2.8.3BifurcationsofMaps

2.9Summary

2.10Exercises

3MathematicalBackground

3.1GroupsandFields

3.2VectorSpaces,Algebras,Norms,andInducedNorms

3.3ContractionMappingTheorems

3.3.1IncrementalSmallGainTheorem

3.4ExistenceandUniquenessTheoremsforOrdinaryDifferentialEquations

3.4.1DependenceonInitialConditionsonInfiniteTimeIntervals

3.4.2CircuitSimulationbyWaveformRelaxation

3.5DifferentialEquationswithDiscontinuities

3.6CarlemanLinearization

3.7DegreeTheory

3.8DegreeTheoryandSolutionsofResistiveNetworks

3.9BasicsofDifferentialTopology

3.9.1SmoothManifoldsandSmoothMaps

3.9.2TangentSpacesandDerivatives

3.9.3RegularValues

3.9.4ManifoldswithBoundary

3.10Summary

3.11Exercises

4Input-OutputAnalysis

5LyapunovStabilityTHeory

6ApplicationsofLyapunovTHeory

7DynamicalSystemsandBifurcations

8BasicsofDifferentialGeometry

9LinearizationbyStateFeedback

10DesignExamplesUsingLinearization

11GeometricNonlinearControl

12ExteriorDifferentialSystemsinControl

13NewVistas:Multi-AgentHybridSystems

References

Index

　　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第一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。