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
Boyd, Stephen
Stephen P. Boyd is the Samsung Professor of Engineering, and Professor of Electrical Engineering in the Information Systems Laboratory at Stanford University. His current research focus is on convex optimization applications in control, signal processing, and circuit design.
Professor Boyd received an AB degree in Mathematics, summa cum laude, from Harvard University in 1980, and a PhD in EECS from U. C. Berkeley in 1985. In 1985 he joined the faculty of Stanford’s Electrical Engineering Department. He has held visiting Professor positions at Katholieke University (Leuven), McGill University (Montreal), Ecole Polytechnique Federale (Lausanne), Qinghua University (Beijing), Universite Paul Sabatier (Toulouse), Royal Institute of Technology (Stockholm), Kyoto University, and Harbin Institute of Technology. He holds an honorary doctorate from Royal Institute of Technology (KTH), Stockholm.
Professor Boyd is the author of many research articles and three books: Linear Controller Design: Limits of Performance (with Craig Barratt, 1991), Linear Matrix Inequalities in System and Control Theory (with L. El Ghaoui, E. Feron, and V. Balakrishnan, 1994), and Convex Optimization (with Lieven Vandenberghe, 2004).
Professor Boyd has received many awards and honors for his research in control systems engineering and optimization, including an ONR Young Investigator Award, a Presidential Young Investigator Award, and an IBM faculty development award. In 1992 he received the AACC Donald P. Eckman Award, which is given annually for the greatest contribution to the field of control engineering by someone under the age of 35. In 1993 he was elected Distinguished Lecturer of the IEEE Control Systems Society, and in 1999, he was elected Fellow of the IEEE, with citation: “For contributions to the design and analysis of control systems using convex optimization based CAD tools.” He has been invited to deliver more than 30 plenary and keynote lectures at major conferences in both control and optimization.
In addition to teaching large graduate courses on Linear Dynamical Systems, Nonlinear Feedback Systems, and Convex Optimization, Professor Boyd has regularly taught introductory undergraduate Electrical Engineering courses on Circuits, Signals and Systems, Digital Signal Processing, and Automatic Control. In 1994 he received the Perrin Award for Outstanding Undergraduate Teaching in the School of Engineering, and in 1991, an ASSU Graduate Teaching Award. In 2003, he received the AACC Ragazzini Education award, for contributions to control education, with citation: “For excellence in classroom teaching, textbook and monograph preparation, and undergraduate and graduate mentoring of students in the area of systems, control, and optimization.”
Handout Name | Handout Usage |
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Cover page and table of contents | |
Overview | Lecture 1 |
Linear functions | Lecture 2-3 |
Linear algebra review | Lectures 3-4 |
Orthonormal sets of vectors and QR factorization | Lecture 4-5 |
Least-squares | Lectures 5-6 |
Least-squares applications | Lectures 6-7 |
Regularized least-squares and Gauss-Newton method | Lectures 7-8 |
Least-norm solutions of underdetermined equations | Lectures 8-9 |
Autonomous linear dynamical systems | Lecture 9 |
Solution via Laplace transform and matrix exponential | Lecture 11 |
Eigenvectors and diagonalization | Lectures 12-13 |
Jordan canonical form | Lectures 13-14 |
Linear dynamical systems with inputs and outputs | Lectures 14-15 |
Example: Aircraft dynamics | Lecture 15 |
Symmetric matrices, quadratic forms, matrix norm, and SVD | Lectures 15-17 |
SVD applications | Lectures 17-18 |
Example: Quantum mechanics | Lecture 18 |
Controllability and state transfer | Lectures 18-20 |
Observability and state estimation | Lecture 20 |
Summary and final comments | Lecture 20 |
All numbered exercises are from the EE263 homework problems.
You will sometimes need to download Matlab files, see Software below.
Assignment | Exercises | Due Date |
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Homework 1 | 2.1–2.4, 2.6, 2.9, 2.12, and an additional exercise | Lecture 4 |
Homework 2 | 3.2, 3.3, 3.10, 3.11, 3.16, 3.17, and three additional exercises | Lecture 6 |
Homework 3 | 2.17, 3.13, 4.1–4.3, 5.1, 6.9, and two additional exercises | Lecture 8 |
Homework 4 | 5.2, 6.2, 6.5, 6.12, 6.14, 6.26, 7.3, 8.2 | Lecture 10 |
Homework 5 | 10.2, 10.3, 10.4, and an additional exercise | Lecture 13 |
Homework 6 | 9.9, 10.5, 10.6, 10.8, 10.14, 11.3, and 11.6a | Lecture 14 |
Homework 7 | 10.9, 10.11, 10.19, 11.13, 12.1, 13.1, and an additional exercise | Lecture 16 |
Homework 8 | 13.17, 14.2, 14.3, 14.4, 14.6, 14.8, 14.9, 14.11, 14.13, 14.21, 14.33, and an additional exercise Please note: (a) you have two weeks to do these, and (b) some of them are very straightforward. |
Lecture 18 |
Homework 9 | 14.16, 14.26, 15.2, 15.3, 15.6, 15.8, 15.10, and 15.11 | Lecture 20 |
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Duration: | |
Watch Now | Download | 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 |
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Watch Now | Download | 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 |
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Watch Now | Download | 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 |
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Duration: | |
Watch Now | Download | 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 |
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Watch Now | Download | 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 |
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Watch Now | Download | 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 |
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Watch Now | Download | 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 |
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Watch Now | Download | 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 |
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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 |
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Watch Now | Download | 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) |
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Watch Now | Download | 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 |
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Watch Now | Download | 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 |
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Watch Now | Download | 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 |
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Watch Now | Download | 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 |
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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 |
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Watch Now | Download | 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 |
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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 |