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Jack Baskin School of EngineeringUC Santa Cruz

CMPE 240 - Introduction to Linear Dynamical Systems - Spring 2017


Final will go out on Friday 9/Jun after class.

If you cannot do the final then, please arrange w/Sharon to pick it up



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:


xdot = A*x +B*u

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.

 

Piazza CMPE240 Home

Handouts

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.

 

  1. Lecture #0, Introduction, 03-Apr-2017
  2. Lecture #1, LinearFunctions, 05-Apr-2017
  3. Lecture #2, LinearFunctions_cont, 07-Apr-2017
  4. Lecture #3, linearAlgebraReview, 10-Apr-2017
  5. Lecture #4, linearAlgebraReview, 12-Apr-2017
  6. Lecture #5, OrthonormalQR, 14-Apr-2017
  7. Lecture #6, OrthonormalQR, 17-Apr-2017
  8. Lecture #7, LeastSquares, 19-Apr-2017
  9. Lecture #8, LeastSquares, 21-Apr-2017
  10. Lecture #9, LeastSquaresApps, 24-Apr-2017
  11. Lecture #10, RegularLeastSquares, 26-Apr-2017
  12. Lecture #11, LeastNorm, 29-Apr-2017
  13. Lecture #12, AutonomousLDS, 01-May-2017
  14. Lecture #13, AutonomousLDS, 03-May-2017
  15. Lecture #14, MatrixExponential, 05-May-2017
  16. Lecture #15, MatrixExponential, 08-May-2017
  17. Lecture #16, Eigenvectors, 11-May-2017
  18. Lecture #17, Eigenvectors, 12-May-2017
  19. Lecture #18, JordanForm, 16-May-2017
  20. Lecture #19, CaleyHamilton, 17-May-2017
  21. Lecture #20, InputOutput, 19-May-2017
  22. Lecture #21, InputOutput, 22-May-2017
  23. Lecture #22, SymmmetricMatrices, 26-May-2017
  24. Lecture #23, PositiveDefinite, 31-May-2017
  25. Lecture #24, SVD, 02-Jun-2017
  26. Lecture #25, SVDApplications, 05-Jun-2017
  27. Lecture #26, Controllability, 06-Jun-2017

 

Homework

Homeworks are posted on the website at the beginning of the week and are due at midnight the following Wednesday. Homeworks will only be accepted in PDF form uploaded to the CANVAS website. You have 48 hours of grace period to be used on homework assignements throught the quarter, late assignments beyond those 48 hours will not be accepted. Cooperation and collaboration on the homeworks is encouraged, but this is NOT licence to copy. The work you turn in should be your own.

 

The link for CANVAS is https://canvas.ucsc.edu/

  1. Homework #1 (Solutions): Introducation to Linear Dynamical Systems, due 12-Apr-2017.
  2. Homework #2 (Solutions): Some Simple Design and Estimation, Due 19-Apr-2017.
  3. Homework #3 (Solutions): QR Factorization and Gram-Schmidt, Due 26-Apr-2017.
  4. Homework #4 (Solutions): Least Squares and Applications, Due 03-May-2017.
  5. Homework #5 (Solutions): Practice Midterm, Due 10-May-2017.
  6. Homework #6 (Solutions): Autonomous LDS and Matrix Exponential, Due 18-May-2017.
  7. Homework #7 (Solutions): Eigenvalues and Eigenvectors, Due 25-Feb-16.
  8. Homework #8 (Solutions): Inputs and Outputs, Due 04-Mar-16.
  9. Homework #9 (Solutions): SVD in all its glory, Due 10-Mar-16.

 

Exams

Midterm scheduled 2PM on Thursday, 11/Feb, 24 Hour take-home exam, Open Book, Notes, etc.
Final scheduled 11:30AM on 09-Jun-2017, 24 Hour take-home exam, due 11:30 AM on 10-Jun-2017, 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.

  1. Lecture #0: Introduction to Linear Dynamical Systems, 03-Apr-2017
  2. Lecture #1, LinearFunctions, 05-Apr-2017
  3. Lecture #2, LinearFunctions_cont, 07-Apr-2017
  4. Lecture #3, linearAlgebraReview, 10-Apr-2017
  5. Lecture #4, linearAlgebraReview_end, 14-Apr-2017
  6. Lecture #5, OrthonormalQR, 14-Apr-2017
  7. Lecture #6, LeastSquares, 19-Apr-2017
  8. Lecture #7, LeastSquaresApps, 24-Apr-2017
  9. Lecture #8, RegularLeastSquares, 26-Apr-2017
  10. Lecture #9, LeastNorm, 28-Apr-2017
  11. Lecture #10, AutonomousLDS, 01-May-2017
  12. Lecture #11, MatrixExponential, 05-May-2017
  13. Lecture #12, Eigenvectors, 10-May-2017
  14. Lecture #13, JordanForm, 15-May-2017
  15. Lecture #14, InputOutput, 19-May-2017
  16. Lecture #15, SymmmetricMatrices, 26-May-2017
  17. Lecture #16, SVDApplications, 05-Jun-2017
  18. Lecture #17, Controllability, 06-Jun-2017
  19. Lecture #18, Observability, 09-Jun-2017

 

 

  1. Office Hours, 06-Apr-2017

General Class Information
Lecture times:
Monday-Wednesday-Friday, 10:40 - 11:45 AM, Porter College - Room 144
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:
T/Th, 9:00 - 11:00 AM, and by appointment