By Stephen Boyd | Introduction to Linear Dynamical Systems Lecture 8 of 20
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
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.
Transcript | Regularized least-squares and Gauss-Newton method | Least-norm solutions of underdetermined equations | Homework 3 | Exercises 2.17, 3.13, 4.1–4.3, 5.1, 6.9
