CMPE 240 - Introduction to Linear Dynamical Systems - Winter 2016
Final rules are in effect--talk to no one!
Practice Final is posted below.
HW #9 is posted, due 10-Mar-2016.
Background
Linear Dynamical Systems (sometimes also called Linear Operator Theory refers to a mathematical representation of a physical system that can be represented by a set of 1st order differential equations or 1st order difference (or recursion) equations for discrete time systems. Generally, these systems can be written in a very simple (and very overloaded form) of:
The study of these linear systems started historically in the 1960's and required a Ph.D. in math as a necessary prerequisite. Most of the applications at the time were to aerospace control problems (such as rocket guidance). Today, these types of systems are studied extensively, and applications range from controls to economics. Frequently, these problems are cast as dual problems: design (where the input vector is altered to reach a desired output) and estimation (where a set a sensor measurements are processed to estimate the state of the system).
Prerequisites
The only prerequisites for this class are exposure to Linear Algebra and Differential Equations (AMS/ENG 27 fulfills these just fine). A class on circuits (EE 70), controls (EE 154/241), signals and systems (EE 103), and/or dynamics (PHYS 5/6) would be useful, but are by no means critical. The only other prerequisites are a willingness to do the work, which will be hard at times.
Acknowledgements
This course is based on the Introduction to Linear Dynamical Systems sequence (EE263 and EE363), offered at Stanford by Professor Stephen Boyd. Lecture notes are taken from his published lecture notes, "EE263: Introduction to Linear Dynamical Systems," Fall 2007.
I would like to acknowledge the tremendous help and generosity of Prof. Stephen Boyd of Stanford University in teaching the subject matter to me, for all of his help with the slides, the homeworks, and the course materials. I would also like to thank Prof. Ed Carryer at Stanford University for pioneering this video capture technology, and helping me to set it up. Without their help and inspiration, this class would not be here.
Index of class resources
- General Class Information class and section times, instructor and TA information
- Lecture Video Video files of the lectures.
- Handouts homework problem sets, homework solutions, other helpful handouts.
- Piazza - for announcements, general discussion, and help.
Piazza
We'll be conducting all class-related discussion on Piazza this term (rather than the web forum).
The quicker you begin asking questions on Piazza (rather than via emails),
the quicker you'll benefit from the collective knowledge of your classmates and instructors.
We encourage you to ask questions when you're struggling to understand a concept.
Handouts
- General Course Information and Syllabus
- Class Flyer
- A Primer on Matrices
- Basic Notation used in CMPE240
- Phase Plane mapping software in MATLAB and Java
- Least Squares in MATLAB
- MIT 18.06 Linear Algebra, for review.
- Homework
- Class Presentation Slides
Lecture Videos
The technology to record these videos is supported by a grant from
the Center for Teaching Excellence (CTE), and it is an experiment. Feedback
as to the utility, and the usability of these videos would be highly
appreciated. The basic hardware required is a tablet PC with a digitizer
(waacom) pen, and a standard headset to capture the lecturer's voice.
Additionally, a program called Camtasia is used to capture the
entire sequence into a standard movie format that can then be viewed
at a later time for review and additional study.
You may view these lectures at any time, but do not distribute them
beyond the UCSC environment. These lectures have been created using
the Camtasia
software, and can be played through
VLC which is cross-platform. Or any other video player of your choice.
- Lecture #0, 05-Jan-2015, Introduction.
- Lecture #1, 07-Jan-2016, Applications and Linear Systems.
- Lecture #2, 12-Jan-2016, Linear Functions and Linear ALgebra Review.
- Lecture #3, 14-Jan-2016, Linear Algebra Review (con't).
- Lecture #4, 19-Jan-2016, QR Decomposition
- Lecture #5, 21-Jan-2016, Least Squares
- Lecture #6, 26-Jan-2016, Least Squares Applications
- Lecture #7, 28-Jan-2016, Least Squares Applications (con't)
- Lecture #8, 02-Feb-2016, Regularized Least Squares
- Lecture #9, 04-Feb-2016, Least Norm
- Lecture #10, 09-Feb-2016, Linear Dynamical Systems
- Lecture #11, 11-Feb-2016, Matrix Exponential
- Lecture #12, 16-Feb-2016, Eigenvalues and Eigenvectors
- Lecture #13, 18-Feb-2016, Diagonalization
- Lecture #14, 23-Feb-2016, Jordan Form
- Lecture #15, 25-Feb-2016, Linear Systems with Input and Output
- Lecture #16, 01-Mar-2016, Discrete vesions of LDS w/IO
- Lecture #17, 03-Mar-2016, Symmetric Matrices
- Lecture #18, 08-Mar-2016, Singular Value Decomposition
- Lecture #19, 10-Mar-2016, SVD Applications and Controllability
- Midterm Review, 09-Feb-2016, Midterm Review (from 2007)
- Final Review, 08-Mar-2016, Final Review (from 2007)
- Office Hours, 11-Jan-2016, Office Hours
- Office Hours, 13-Jan-2016, Office Hours
- Office Hours, 19-Jan-2016, Office Hours
- Office Hours, 20-Jan-2016, Office Hours
- Office Hours, 27-Jan-2016, Office Hours
- Office Hours, 03-Feb-2016, Office Hours
- Office Hours, 10-Feb-2016, Office Hours
- Office Hours, 24-Feb-2016, Office Hours
- Office Hours, 02-Mar-2016, Office Hours
- Office Hours, 09-Mar-2016, Office Hours
Homework
Homeworks are handed out in class, and are due back either in class or in
my office, 337B Engineering 2, at 5 PM on the following
week. Homeworks will only be accepted at the beginning of class, not
at the end of class. Homeworks turned in late will be receive half the
total points once the solution set has been posted. Cooperation and
collaboration on the homeworks is encouraged, but this is NOT
licence to copy. The work you turn in should be your own.
- Homework #1 (Solutions): Introducation to Linear Dynamical Systems, due 14-Jan-16.
- Homework #2 (Solutions): Some Simple Design and Estimation, Due 21-Jan-16.
- Homework #3 (Solutions): QR Factorization and Gram-Schmidt, Due 28-Jan-16.
- Homework #4 (Solutions): Least Squares and Applications, Due 04-Feb-16.
- Homework #5 (Solutions): Practice Midterm, Due 11-Feb-16.
- Homework #6 (Solutions): Autonomous LDS and Matrix Exponential, Due 18-Feb-16.
- Homework #7 (Solutions): Eigenvalues and Eigenvectors, Due 25-Feb-16.
- Homework #8 (Solutions): Inputs and Outputs, Due 04-Mar-16.
- Homework #9 (Solutions): SVD in all its glory, Due 10-Mar-16.
We'll be conducting all class-related discussion on Piazza this term (rather than the web forum). The quicker you begin asking questions on Piazza (rather than via emails), the quicker you'll benefit from the collective knowledge of your classmates and instructors. We encourage you to ask questions when you're struggling to understand a concept.
The technology to record these videos is supported by a grant from the Center for Teaching Excellence (CTE), and it is an experiment. Feedback as to the utility, and the usability of these videos would be highly appreciated. The basic hardware required is a tablet PC with a digitizer (waacom) pen, and a standard headset to capture the lecturer's voice. Additionally, a program called Camtasia is used to capture the entire sequence into a standard movie format that can then be viewed at a later time for review and additional study.
You may view these lectures at any time, but do not distribute them beyond the UCSC environment. These lectures have been created using the Camtasia software, and can be played through VLC which is cross-platform. Or any other video player of your choice.
Homeworks are handed out in class, and are due back either in class or in my office, 337B Engineering 2, at 5 PM on the following week. Homeworks will only be accepted at the beginning of class, not at the end of class. Homeworks turned in late will be receive half the total points once the solution set has been posted. Cooperation and collaboration on the homeworks is encouraged, but this is NOT licence to copy. The work you turn in should be your own.
- color_perception.m, required for homework #2.
- inductor_data.m, required for homework #3.
- deconv_data.m, required for homework #3.
- emissions_data.m, required for homework #4.
- sig_est_data.m, required for practice midterm/homework #5.
- directed_graph.m, required for practice midterm/homework #5.
- gauss_fit_data.m, required for homework #7.
- interconn.m, required for homework #8.
- time_comp_data.m, required for homework #8.
- mc_data.m, required for practice final.
- nleq_data.m, required for practice final.
- temp_prof_data.m, required for practice final.
- tv_data.mm, required for practice final.
Exams
Midterm scheduled 2PM on Thursday, 11/Feb, 24 Hour take-home exam, Open Book, Notes, etc.
Final scheduled 10 AM on 17-Mar-2016, 24 Hour take-home exam, due 10 AM on 18-Mar-2016, Open Book, Notes, etc.
Class Presentation Slides
The class lectures use the digital ink capabilities of the TabletPC. The ink is saved back into the presentation, and the presentation is saved to the website for convenience. This year we are using Classroom Presenter 3 as it has several nice utilities for the TabletPC. The presentation files are in .PDF format.
- Lecture #0: Introduction to Linear Dynamical Systems, 05-Jan-16
- Lecture #1: Linear Functions and Applications, 07-Jan-16
- Lecture #2: Linear Algebra Review, 12-Jan-16
- Lecture #3: Linear Algebra Review (con't), 14-Jan-16
- Lecture #4: QR Factorization, 19-Jan-16
- Lecture #5: Least Squares, 21-Jan-2016
- Lecture #6: Least Squares Applications, 26-Jan-2016
- Lecture #7: Least Squares Applications, 28-Jan-2016
- Lecture #8: Regularized Least Squares, 02-Feb-2016.
- Lecture #9: Least Norm, 04-Feb-2016.
- Lecture #10: Autonomous LDS, 09-Feb-2016
- Lecture #11: Matrix Exponential, 11-Feb-2016
- Lecture #12: Eigenvectors, 16-Feb-2016
- Lecture #13: Diagnolization, 18-Feb-2016
- Lecture #14: Jordan Form, 23-Feb-2016
- Lecture #15: Input Output, 25-Feb-2016
- Lecture #16: Discrete versions of LDS w/IO, 01-Mar-2016
- Lecture #17: Symmetric Matrices, 03-Mar-2016
- Lecture #18: Singular Value Decomposition, 08-Mar-2016
- Lecture #19, 10-Mar-2016, SVD Applications and Controllability
- Midterm Review, 09-Feb-2016 (from 2007)
- Final Review, 08-Mar-2016 (from 2007)
- Office Hours 11-Jan-2016
- Office Hours 13-Jan-2016, (sorry, annotations lost)
- Office Hours 19-Jan-2016
- Office Hours 20-Jan-2016
- Office Hours 27-Jan-2016
- Office Hours 03-Feb-2016
- Office Hours 10-Feb-2016
- Office Hours 24-Feb-2016
- Office Hours 02-Mar-2016
- Office Hours 09-Mar-2016
- Textbooks: note that these are NOT required, but are excellent references
- "Linear Algebra and its Applications, 3rd Ed." by Gilbert Strang, Brooks Cole, 1988. ISBN: 0155510053.
- Lecture Notes for Stanford's EE263 Class, by Steve Boyd, 2008/2009
- Instructor:
- Name: Gabriel Hugh Elkaim (elkaim@soe.ucsc.edu)
- Phone: 831-459-3054
- Office: Engineering 2, 337B
- Instructor Office Hours:
- Wed, 1:00 - 3:00 PM, and by appointment