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دوره آشنایی با سیستم های داینامیک خطی دانشگاه Stanford

دسته بندی ها: دانشگاه استنفورد (Stanford)

دوره-آشنایی-با-سیستم-های-داینامیک-خطی-د

دوره آشنایی با سیستم های داینامیکی خطی (Introduction To Linear Dynamical Systems) توسط پروفسور Stephen Boyd در دانشگاه Stanford تدریس شده است.

در این دوره آموزشی با اصول سیستم های داینامیک خطی آشنا می شوید.

سرفصل های دوره:

  • Overview Of Linear Dynamical Systems
  • Linear Functions
  • Linearization
  • Nullspace Of A Matrix
  • Orthonormal Set Of Vectors
  • Least-Squares
  • Geometric Interpretation
  • Least-Squares (Approximate) Solution
  • Least-Squares Polynomial Fitting
  • Multi-Objective Least-Squares
  • Weighted-Sum Objective
  • Minimizing Weighted-Sum Objective
  • Least-Norm Solution
  • Examples Of Autonomous Linear Dynamical Systems
  • Solution Via Laplace Transform And Matrix Exponential
  • Time Transfer Property
  • Markov Chain (Example)
  • Jordan Canonical Form
  • DC Or Static Gain Matrix
  • RC Circuit (Example)
  • Gain Of A Matrix In A Direction
  • Sensitivity Of Linear Equations To Data Error
  • Reachability
  • Continuous-Time Reachability

Lecture 1
1 hr 17 min
Topics: Overview Of Linear Dynamical Systems, Why Study Linear Dynamical Systems?, Examples Of Linear Dynamical Systems, Estimation/Filtering Example, Linear Functions And Examples

Lecture 2 1 hr 6 min Topics: Linear Functions (Continued), Interpretations Of Y=Ax, Linear Elastic Structure, Example, Total Force/Torque On Rigid Body Example, Linear Static Circuit Example, Illumination With Multiple Lamps Example, Cost Of Production Example, Network Traffic And Flow Example, Linearization And First Order Approximation Of Functions

Lecture 3 1 hr 19 min Topics: Linearization (Continued), Navigation By Range Measurement, Broad Categories Of Applications, Matrix Multiplication As Mixture Of Columns, Block Diagram Representation, Linear Algebra Review, Basis And Dimension, Nullspace Of A Matrix

Lecture 4 1 hr 14 min Topics: Nullspace Of A Matrix(Continued), Range Of A Matrix, Inverse, Rank Of A Matrix, Conservation Of Dimension, 'Coding' Interpretation Of Rank, Application: Fast Matrix-Vector Multiplication, Change Of Coordinates, (Euclidian) Norm, Inner Product, Orthonormal Set Of Vectors

Lecture 5 1 hr 15 min Topics: Orthonormal Set Of Vectors, Geometric Interpretation, Gram-Schmidt Procedure, General Gram-Schmidt Procedure, Applications Of Gram-Schmidt Procedure, 'Full' QR Factorization, Orthogonal Decomposition Induced By A, Least-Squares

Lecture 6 1 hr 16 min Topics: Least-Squares, Geometric Interpretation, Least-Squares (Approximate) Solution, Projection On R(A), Least-Squares Via QR Factorization, Least-Squares Estimation, Blue Property, Navigation From Range Measurements, Least-Squares Data Fitting

Lecture 7 1 hr 16 min Topics: Least-Squares Polynomial Fitting, Norm Of Optimal Residual Versus P, Least-Squares System Identification, Model Order Selection, Cross-Validation, Recursive Least-Squares, Multi-Objective Least-Squares

Lecture 8 1 hr 16 min Topics: Multi-Objective Least-Squares, Weighted-Sum Objective, Minimizing Weighted-Sum Objective, Regularized Least-Squares, Laplacian Regularization, Nonlinear Least-Squares (NLLS), Gauss-Newton Method, Gauss-Newton Example, Least-Norm Solutions Of Undetermined Equations

Lecture 9 1 hr 9 min Topics: Least-Norm Solution, Least-Norm Solution Via QR Factorization, Derivation Via Langrange Multipliers, Example: Transferring Mass Unit Distance, Relation To Regularized Least-Squares, General Norm Minimization With Equality Constraints, Autonomous Linear Dynamical Systems, Block Diagram

Lecture 10 1 hr 12 min Topics: Examples Of Autonomous Linear Dynamical Systems, Finite-State Discrete-Time Markov Chain, Numerical Integration Of Continuous System, High Order Linear Dynamical Systems, Mechanical Systems, Linearization Near Equilibrium Point, Linearization Along Trajectory

Lecture 11 1 hr 9 min Topics: Solution Via Laplace Transform And Matrix Exponential, Laplace Transform Solution Of X_^ = Ax, Harmonic Oscillator Example, Double Integrator Example, Characteristic Polynomial, Eigenvalues Of A And Poles Of Resolvent, Matrix Exponential, Time Transfer Property

Lecture 12 1 hr 14 min Topics: Time Transfer Property, Piecewise Constant System, Qualitative Behavior Of X(T), Stability, Eigenvectors And Diagonalization, Scaling Interpretation, Dynamic Interpretation, Invariant Sets, Summary, Markov Chain (Example)

Lecture 13 1 hr 13 min Topics: Markov Chain (Example), Diagonalization, Distinct Eigenvalues, Digaonalization And Left Eigenvectors, Modal Form, Diagonalization Examples, Stability Of Discrete-Time Systems, Jordan Canonical Form, Generalized Eigenvectors

Lecture 14 1 hr 18 min Topics: Jordan Canonical Form, Generalized Modes, Cayley-Hamilton Theorem, Proof Of C-H Theorem, Linear Dynamical Systems With Inputs & Outputs, Block Diagram, Transfer Matrix, Impulse Matrix, Step Matrix

Lecture 15 1 hr 9 min Topics: DC Or Static Gain Matrix, Discretization With Piecewise Constant Inputs, Causality, Idea Of State, Change Of Coordinates, Z-Transform, Symmetric Matrices, Quadratic Forms, Matrix Nom, And SVD, Eigenvalues Of Symmetric Matrices, Interpretations Of Eigenvalues Of Symmetric Matrices, Example: RC Circuit

Lecture 16 1 hr 13 min Topics: RC Circuit (Example), Quadratic Forms, Examples Of Quadratic Form, Inequalities For Quadratic Forms, Positive Semidefinite And Positive Definite Matrices, Matrix Inequalities, Ellipsoids, Gain Of A Matrix In A Direction, Matrix Norm, Properties Of Matrix Norm

Lecture 17 1 hr 17 min Topics: Gain Of A Matrix In A Direction, Singular Value Decomposition, Interpretations, Singular Value Decomposition (SVD) Applications, General Pseudo-Inverse, Pseudo-Inverse Via Regularization, Full SVD, Image Of Unit Ball Under Linear Transformation, SVD In Estimation/Inversion, Sensitivity Of Linear Equations To Data Error

Lecture 18 1 hr 15 min Topics: Sensitivity Of Linear Equations To Data Error, Low Rank Approximations, Distance To Singularity, Application: Model Simplification, Controllability And State Transfer, State Transfer, Reachability, Reachability For Discrete-Time LDS

Lecture 19 1 hr 10 min Topics: Reachability, Controllable System, Lest-Norm Input For Reachability, Minimum Energy Over Infinite Horizon, Continuous-Time Reachability, Impulsive Inputs, Least-Norm Input For Reachability

Lecture 20 1 hr 9 min Topics: Continuous-Time Reachability, General State Transfer, Observability And State Estimation, State Estimation Set Up, State Estimation Problem, Observability Matrix, Least-Squares Observers, Some Parting Thoughts..., Linear Algebra, Levels Of Understanding, What's Next

عنوان دوره: Stanford University Introduction To Linear Dynamical Systems حجم فایل:4.8GB

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Stanford University Introduction to Linear Dynamical Systems

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