斯坦福大學開放課程 線性動力系統緒論 Open Stanford Course Introduction to Linear Dynamical Systems 英文版 DVD 只於電腦播放 斯坦福大學的“StanfordEngineeringEverywhere”免費提供學校裡最受歡迎的工科課程，給全世界的學生和教育工作者。 得益於這個項目，我們有機會和全世界站在同一個數量級的知識起跑線上。 本課程系列內容來源於斯坦福大學的“StanfordEngineeringEverywhere”項目。 官網地址：http://see.stanford.edu/default.aspx 斯坦福大學開放課程:線性動力系統課程課程代號EE263 OpenStanfordCourse:IntroductiontoLinearDynamicalSystems 主講:StephenBoyd 課程介紹: 線性動力系統（EE263）介紹應用線性代數和線性動力系統，與應用電路，信號處理，通信和控制系統。主題包括：最小二乘aproximations的超定方程和最不規範的解決方案的underdetermined方程。對稱矩陣，矩陣範數和奇異值分解。特徵值，左，右特徵向量，和動態的解釋。矩陣指數，穩定和漸近性。多輸入多輸出系統，衝動和步驟矩陣;卷積和轉移矩陣描述。控制，可達性，狀態轉移，和最不規範的投入。觀測和最小二乘狀態估計。 CourseDescription Introductiontoappliedlinearalgebraandlineardynamicalsystems,withapplicationstocircuits,signalprocessing,communications,andcontrolsystems. Topicsinclude:Least-squaresaproximationsofover-determinedequationsandleast-normsolutionsofunderdeterminedequations.Symmetricmatrices,matrixnormandsingularvaluedecomposition.Eigenvalues,leftandrighteigenvectors,anddynamicalinterpretation.Matrixexponential,stability,andasymptoticbehavior.Multi-inputmulti-outputsystems,impulseandstepmatrices;convolutionandtransfermatrixdescriptions.Control,reachability,statetransfer,andleast-norminputs.Observabilityandleast-squaresstateestimation. Prerequisites:Exposuretolinearalgebraandmatrices.Youshouldhaveseenthefollowingtopics:matricesandvectors,(introductory)linearalgebra;differentialequations,Laplacetransform,transferfunctions.Exposuretotopicssuchascontrolsystems,circuits,signalsandsystems,ordynamicsisnotrequired,butcanincreaseyourappreciation. 目錄: 課程主要內容預覽 Lecture1-OverviewOfLinearDynamicalSystems OverviewOfLinearDynamicalSystems,WhyStudyLinearDynamicalSystems?,ExamplesOfLinearDynamicalSystems,Estimation/FilteringExample,LinearFunctionsAndExamples Lecture2-LinearFunctions(Continued) LinearFunctions(Continued),InterpretationsOfY=Ax,LinearElasticStructure,Example,TotalForce/TorqueOnRigidBodyExample,LinearStaticCircuitExample,IlluminationWithMultipleLampsExample,CostOfProductionExample,NetworkTrafficAndFlowExample,LinearizationAndFirstOrderApproximationOfFunctions Lecture3-Linearization(Continued) Linearization(Continued),NavigationByRangeMeasurement,BroadCategoriesOfApplications,MatrixMultiplicationAsMixtureOfColumns,BlockDiagramRepresentation,LinearAlgebraReview,BasisAndDimension,NullspaceOfAMatrix Lecture4-NullspaceOfAMatrix(Continued) NullspaceOfAMatrix(Continued),RangeOfAMatrix,Inverse,RankOfAMatrix,ConservationOfDimension,'Coding'InterpretationOfRank,Application:FastMatrix-VectorMultiplication,ChangeOfCoordinates,(Euclidian)Norm,InnerProduct,OrthonormalSetOfVectors Lecture5-OrthonormalSetOfVectors OrthonormalSetOfVectors,GeometricInterpretation,Gram-SchmidtProcedure,GeneralGram-SchmidtProcedure,ApplicationsOfGram-SchmidtProcedure,'Full'QRFactorization,OrthogonalDecompositionInducedByA,Least-Squares Lecture6-Least-Squares Least-Squares,GeometricInterpretation,Least-Squares(Approximate)Solution,ProjectionOnR(A),Least-SquaresViaQRFactorization,Least-SquaresEstimation,BlueProperty,NavigationFromRangeMeasurements,Least-SquaresDataFitting Lecture7-Least-SquaresPolynomialFitting Least-SquaresPolynomialFitting,NormOfOptimalResidualVersusP,Least-SquaresSystemIdentification,ModelOrderSelection,Cross-Validation,RecursiveLeast-Squares,Multi-ObjectiveLeast-Squares Lecture8-Multi-ObjectiveLeast-Squares Multi-ObjectiveLeast-Squares,Weighted-SumObjective,MinimizingWeighted-SumObjective,RegularizedLeast-Squares,LaplacianRegularization,NonlinearLeast-Squares(NLLS),Gauss-NewtonMethod,Gauss-NewtonExample,Least-NormSolutionsOfUndeterminedEquations Lecture9-Least-NormSolution Least-NormSolution,Least-NormSolutionViaQRFactorization,DerivationViaLangrangeMultipliers,Example:TransferringMassUnitDistance,RelationToRegularizedLeast-Squares,GeneralNormMinimizationWithEqualityConstraints,AutonomousLinearDynamicalSystems,BlockDiagram favorites Lecture10-ExamplesOfAutonomousLinearDynamicalSystems ExamplesOfAutonomousLinearDynamicalSystems,Finite-StateDiscrete-TimeMarkovChain,NumericalIntegrationOfContinuousSystem,HighOrderLinearDynamicalSystems,MechanicalSystems,LinearizationNearEquilibriumPoint,LinearizationAlongTrajectory Lecture11-SolutionViaLaplaceTransformAndMatrixExponential SolutionViaLaplaceTransformAndMatrixExponential,LaplaceTransformSolutionOfX_^=Ax,HarmonicOscillatorExample,DoubleIntegratorExample,CharacteristicPolynomial,EigenvaluesOfAAndPolesOfResolvent,MatrixExponential,TimeTransferProperty Lecture12-TimeTransferProperty TimeTransferProperty,PiecewiseConstantSystem,QualitativeBehaviorOfX(T),Stability,EigenvectorsAndDiagonalization,ScalingInterpretation,DynamicInterpretation,InvariantSets,Summary,MarkovChain(Example) Lecture13-MarkovChain(Example) MarkovChain(Example),Diagonalization,DistinctEigenvalues,DigaonalizationAndLeftEigenvectors,ModalForm,DiagonalizationExamples,StabilityOfDiscrete-TimeSystems,JordanCanonicalForm,GeneralizedEigenvectors Lecture14-JordanCanonicalForm JordanCanonicalForm,GeneralizedModes,Cayley-HamiltonTheorem,ProofOfCHTheorem,LinearDynamicalSystemsWithInputs&Outputs,BlockDiagram,TransferMatrix,ImpulseMatrix,StepMatrix Lecture15-DCOrStaticGainMatrix DCOrStaticGainMatrix,DiscretizationWithPiecewiseConstantInputs,Causality,IdeaOfState,ChangeOfCoordinates,Z-Transform,SymmetricMatrices,QuadraticForms,MatrixNom,AndSVD,EigenvaluesOfSymmetricMatrices,InterpretationsOfEigenvaluesOfSymmetricMatrices,Example:RCCircuit Lecture16-RCCircuit(Example) RCCircuit(Example),QuadraticForms,ExamplesOfQuadraticForm,InequalitiesForQuadraticForms,PositiveSemidefiniteAndPositiveDefiniteMatrices,MatrixInequalities,Ellipsoids,GainOfAMatrixInADirection,MatrixNorm,PropertiesOfMatrixNorm Lecture17-GainOfAMatrixInADirection GainOfAMatrixInADirection,SingularValueDecomposition,Interpretations,SingularValueDecomposition(SVD)Applications,GeneralPseudo-Inverse,Pseudo-InverseViaRegularization,FullSVD,ImageOfUnitBallUnderLinearTransformation,SVDInEstimation/Inversion,SensitivityOfLinearEquationsToDataError Lecture18-SensitivityOfLinearEquationsToDataError SensitivityOfLinearEquationsToDataError,LowRankApproximations,DistanceToSingularity,Application:ModelSimplification,ControllabilityAndStateTransfer,StateTransfer,Reachability,ReachabilityForDiscrete-TimeLDS Lecture19-Reachability Reachability,ControllableSystem,Lest-NormInputForReachability,MinimumEnergyOverInfiniteHorizon,Continuous-TimeReachability,ImpulsiveInputs,Least-NormInputForReachability Lecture20-Continuous-TimeReachability Continuous-TimeReachability,GeneralStateTransfer,ObservabilityAndStateEstimation,StateEstimationSetUp,StateEstimationProblem,ObservabilityMatrix,Least-SquaresObservers,SomePartingThoughts...,LinearAlgebra,LevelsOfUnderstanding,What'sNext