EECE 7200 Linear Systems
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Instructor: |
Gilead Tadmor |
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Tel. |
617.373.5277 |
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Skype: |
gilead_t (please indicate that you are an EECE 7200 student) |
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Office: |
414 DA |
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Classroom: |
Class participation & office hours: Students are very strongly encouraged to ask questions in class immediately as they arise, and utilize office hours for questions that remain unanswered. Active participation will be highly valued and considered in final grading.
Office Hours: Tuesday and Friday
1. Class students: 1:30 – 2:30 PM.
2. Video Streaming Students: 2:45 – 4 PM.
3. By appointment, following phone / in person schedule.
TA name: Afsaneh Ghanavati
TA Email: afsanehg@ece.neu.edu
E-mail policy:
1. I am dyslexic and find email a difficlut and inefficient communication medium. If you want a timely answer, please contact me in class, by phone or by skype during normal office hours. (Please do not call after 6 pm, even if you believe that I am in my office.)
2. Email to me should be used only regarding procedural matters, and only as a last resort. To receive an answer, the subject line must be “7200student” (no space) and the message should be brief. I will not read or answer emails with other subject lines or long messages.
3. Email to the TA should be used only regarding urgent, procedural matters that cannot be delayed till the next class meeting. These emails too should be brief and have the subject “7200student”.
4. Answers to questions on class material will not be provided by email.
5. Homework may be submitted only by uploading to blackboard. Emailed homework will be accepted only in exceptional pre-approved cases.
Honesty and integrity are paramount: You may consult any publicly available written material and are encouraged to form study groups. However, you are NOT allowed to jointly prepare homework assignments and answers to take home exams, or to consult with any person other the instructor and the TA, regarding these assignments. Cheating is a poor strategy for long-term success. When caught, it will be addressed according to the University Academic Integrity Policy.
Text: W. L. Brogan, Modern Control Theory (3rd Ed.), Prentice-Hall, 1991 (ISBN: 0-13-589763-7)
Class Material: I will post technical on blackboard all handouts, homework assignments, exams, solutions of homework solutions and announcements; please check blackboard regularly!
Supplementary Material: The most productive way to get answers for questions you have on course material is to ask questions in class and during office hours. Looking frantically for understanding by searching additional books in the library is usually a very poor and ineffective course of action. Supplementary material may be very useful to gain a broader and deeper understanding. Books in advanced linear algebra, applied functional analysis, operator theory, linear systems may be helpful this way.
Course Objectives: An introduction to least-mean-squares optimization and linear input/output systems, using state space methods. A user-level understanding of related concepts in advanced algebra, applied functional analysis and operator theory is an essential component of that objective, and indeed, for R&D activities in the wide area spanning digital signal processing (DSP) and Imaging, Communication, Information Theory, Data Mining and Machine Learning, and Control Systems, to name a few examples.
Course Description: The course begins with a review of topics in advanced linear algebra and mathematical analysis, including algebraic, geometric and topological aspects of vector spaces and linear operators; inner products and projections, least mean squares (LMS) approximations and linear-quadratic (LQ) optimization; matrices, Jordan forms and singular value decomposition (SVD). Using these tools, we shall discuss linear input/output (IO) dynamical systems, including state space descriptions and canonical representations, solutions of state equations, stability, concepts and measures of controllability and observability, controller and observer design and optimization.
Course outlines by topical areas:
· Introduction: what linear systems are about.
· Vector spaces: finite and infinite dimensional (signal) spaces, bases and coordinates.
· Linear transformations: basic concepts, matrix representations, similarity transformations, spectral theory (Jordan forms).
· Vector norms and inner products: distance, convergence, orthogonality, projections, least squares approximations and Fourier expansions.
· Operator and matrix norms: approximations, singular value decomposition (SVD) and simple estimation problems.
· State space representations of continuous & discrete time systems: the concept of a state variable, state equations and their solutions.
· Relationships between state variables and transfer function representations.
· Stability: different definitions, connections to Jordan form analysis, operator theoretical formulation, Lyapunov stability.
· Controllability and Observability: basic definitions, geometric and algebraic analysis, Grammians and optimization, canonical forms
· Controller and observer design, relations to basic LMS optimization problem
Computer skills and access: The use MATLAB is an absolute requirement in homework assignments and in exams.
Homework & Take Home Exam Procedures & Guidelines:
· Homework & exam problems and solutions will be posted in .pdf format on blackboard. Latex source files of problem sets will also be posted.
· Homework will be accepted only as a .pdf document. Handwritten homework or homework submitted in other text formats (such as Microsoft word) will not be accepted.
· Solutions are due one week from the day of assignment. A solution handout will be posted after the due date. Late homework submission will not be accepted without prior arrangement with the instructor, or justifiable, clearly unavoidable hindrance.
· Missing more than two homework assignments will prevent a passing grade in the course.
· Homework should be uploaded to blackboard. Emailed homework will be accepted only in exceptional pre-approved cases.
· You will be required to use MATLAB numerical software. Doing so, remember that you may not use library functions when the homework or exam problem requires that you demonstrate your ability to generate the necessary algorithm. When in doubt, write your own algorithms!
· Being able to communicate effectively is especially important in both industry and academe This applies to your homework and exams:
o Answers must be complete: a mere statement of fact, number or formula, without a proof or ample justification is insufficient. Such answers may be ignored and not be graded.
o Answers must be concise: long and verbose explanations is tedious to read and decipher; it will often be ignored in the workplace, and it may meet the same fate during grading, in this class.
o Computer programs are not acceptable as substitutes for verbal answers: A code may be included only as an Appendix to a complete and concise answer, explaining and justifying what you did.
o Computer programs and diaries of their runs must be included in an Appendix: A clearly written and well commented code of programs you use must be included as an Appendix to your solution, whenever such programs are used, along with a diary of the run that produced your answers. The results of computations will not be accepted without such an appendix. Disorganized and unclear programs that are neither explained in the body of an answer, nor clearly organized and commented, will be ignored.
· Grading: Grades will be based on several homework assignments (20%) and two take-home exams (40% each)