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《斯坦福大学开放课程 : 线性动力系统绪论》(Open Stanford Course : Introduction to Linear Dynamical Systems)开放式课程 更新完毕[MP4]

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  • 摘要:
    课程类型物理
    主讲人Stephen Boyd
    发行日期2008年
    对白语言日语
    文字语言英文
  • 时间: 2010/07/26 23:49:01 发布 | 2010/08/06 21:16:45 更新
  • 分类: 教育  理工科 

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中文名斯坦福大学开放课程 : 线性动力系统绪论
英文名Open Stanford Course : Introduction to Linear Dynamical Systems
资源格式MP4
课程类型物理
学校Stanford
斯坦福大学
主讲人Stephen Boyd
版本开放式课程 更新完毕
发行日期2008年
地区美国
对白语言日语
文字语言英文
简介

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发布说明 这个课程VC上以前有网友发布过前6集 由于某些原因不能继续更新
所以我去斯坦福大学官网下载该课程视频 会陆续全部更新上来


资源简介:

斯坦福大学的“Stanford Engineering Everywhere ”免费提供学校里最受欢迎的工科课程,给全世界的学生和教育工作者。
得益于这个项目,我们有机会和全世界站在同一个数量级的知识起跑线上。
本课程系列内容来源于斯坦福大学的“Stanford Engineering Everywhere ”项目。
官网地址: http://see.stanford.edu/default.aspx

斯坦福大学开放课程 : 线性动力系统课程 课程代号EE263
Open Stanford Course : Introduction to Linear Dynamical Systems
主讲: Stephen Boyd
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课程介绍:

线性动力系统( EE263 )介绍应用线性代数和线性动力系统,与应用电路,信号处理,通信和控制系统。主题包括:最小二乘aproximations的超定方程和最不规范的解决方案的underdetermined方程。对称矩阵,矩阵范数和奇异值分解。特征值,左,右特征向量,和动态的解释。矩阵指数,稳定和渐近性。多输入多输出系统,冲动和步骤矩阵;卷积和转移矩阵描述。控制,可达性,状态转移,和最不规范的投入。观测和最小二乘状态估计。

Course Description
Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems.

Topics include: Least-squares aproximations of over-determined equations and least-norm solutions of underdetermined equations. Symmetric matrices, matrix norm and singular value decomposition. Eigenvalues, left and right eigenvectors, and dynamical interpretation. Matrix exponential, stability, and asymptotic behavior. Multi-input multi-output systems, impulse and step matrices; convolution and transfer matrix descriptions. Control, reachability, state transfer, and least-norm inputs. Observability and least-squares state estimation.

Prerequisites: Exposure to linear algebra and matrices. You should have seen the following topics: matrices and vectors, (introductory) linear algebra; differential equations, Laplace transform, transfer functions. Exposure to topics such as control systems, circuits, signals and systems, or dynamics is not required, but can increase your appreciation.

课程视频预览:
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目录

课程主要内容预览
Lecture 1 - Overview Of Linear Dynamical Systems
Overview Of Linear Dynamical Systems, Why Study Linear Dynamical Systems?, Examples Of Linear Dynamical Systems, Estimation/Filtering Example, Linear Functions And Examples

Lecture 2 - Linear Functions (Continued)
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 - Linearization (Continued)
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 - Nullspace Of A Matrix (Continued)
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 - Orthonormal Set Of Vectors
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 - Least-Squares
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 - Least-Squares Polynomial Fitting
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 - Multi-Objective Least-Squares
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 - Least-Norm Solution
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

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Lecture 10 - Examples Of Autonomous Linear Dynamical Systems
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 - Solution Via Laplace Transform And Matrix Exponential
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 - Time Transfer Property
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 - Markov Chain (Example)
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 - Jordan Canonical Form
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 - DC Or Static Gain Matrix
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 - RC Circuit (Example)
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 - Gain Of A Matrix In A Direction
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 - Sensitivity Of Linear Equations To Data Error
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 - Reachability
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 - Continuous-Time Reachability
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

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