讲师信息

Stephen P. Boyd 斯坦福大学 教授

视频简介

    线性动力系统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。

    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.


课程目录

    1.Overview Of Linear Dynamical Systems

    线性动力系统绪论

    2.Linear Functions (Continued)

    线性函数（续）

    3.Linearization (Continued)

    线性线性（续）

    4.Nullspace Of A Matrix (Continued)

    矩阵A的零空间（续）

    5.Orthonormal Set Of Vectors

    正交向量集

    6.Least-Squares

    最小二乘法

    7.Least-Squares Polynomial Fitting

    最小二乘多项式拟合

    8.Multi-Objective Least-Squares

    多目标最小二乘

    9.Least-Norm Solution

    最小范数解

    10.Examples Of Autonomous Linear Dynamical Systems

    线性自治系统举例

    11.Solution Via Laplace Transform And Matrix Exponential

    拉普拉斯变换解法和矩阵指数

    12.Time Transfer Property

    时间迁移

    13.Markov Chain (Example)
    马尔可夫链
    14.Jordan Canonical Form

    Jordan canonical form

    15.DC Or Static Gain Matrix

    DC或静态增益矩阵

    16.RC Circuit (Example)

    RC电路

    17.Gain Of A Matrix In A Direction

    获得矩阵方向

    18.Sensitivity Of Linear Equations To Data Error

    线性方程灵敏度的数据错误

    19.Reachability

    可达

    20.Continuous-Time Reachability
    连续时间可达