Syllabus Electrical Engineering Department EE 653: Robust Control – Semester 182 Scheduled Meeting Times

Type Class

Time 6:45-8 PM

Days MW

Where B 59-1007

Date Range Jan 6th – May 1st, 2019

Schedule Type Lecture

Instructors Dr. SALIM IBRIR

Instructor Dr. Salim Ibrir - B-59-1076, G floor - Email: [email protected] Office Hours: UTR from 10:30 am to 11:30 am I am available 15 min after the lecture or by appointment Course Content: Elements of robust control theory. Norms of signals and systems. Performance specifications. Modeling of uncertain linear systems and system parameterization. Model uncertainty and robustness. Polytopic uncertainties and norm-bounded uncertainties. Domain stability, 𝐻∞ norm, and 𝐻2 norm. Linear matrix inequalities and their numerical solutions. Stability of uncertain linear systems in continuous time and discrete time. 𝐻∞ Filtering, Loop transfer recovery. 𝐻∞ Control, Mixed 𝐻2 − 𝐻∞ control. Case studies. Text: 1. J. B. Burl, Linear optimal control, 𝐻2 and 𝐻∞ methods, Addison-Wesley, 1999. 2. K. Zhou, J. Doyle, and K. Glover. Robust and Optimal Control. Prentice Hall, Englewood Cliffs, New Jersey, 1996. 3. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Volume 15 of Studies in Applied Mathematics Society for Industrial and Applied Mathematics (SIAM), 1994. Available on-line: https://web.stanford.edu/~boyd/lmibook/ Other texts and publications: 1. Katsuhiko Ogata, Matlab for control engineers, Prentice Hall, 2008. 2. Brian D. O. Anderson, and John B. Moore, Optimal control: linear quadratic methods, Prentice Hall International, Inc, 1989. 3. Arthur E. Bryson Jr., and Yu-Chi Ho, Applied optimal control, optimization, estimation, and control, Taylor & Francis, 1975. 4. G. Chesi. LMI techniques for optimization over polynomials in control: a survey, IEEE Transactions on Automatic Control, 55(11):2500–2510, 2010. 5. S. Ibrir, Convex optimization approach to observer-based stabilization of uncertain linear systems, Transactions of the ASME, Journal of Dynamic Systems,

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Measurement and Control, Vol. 128, pp. 989-994, December 2006. (Available on the web site of the Instructor). S. Ibrir, Design of static and dynamic output feedback controllers through Euler approximate models: Uncertain systems with norm-bounded uncertainties, IMA Journal of Mathematical Control and Information, Elsevier, Vol. 25, pp. 281-296, 2008. S. Ibrir and S. Diop, Novel LMI conditions for observer-based stabilization of Lipschitzian nonlinear systems and uncertain linear systems in discrete-time, Applied Mathematics and Computation, Vol. 206, no. 2, pp. 579-588, December 2008. B. Barmish. Necessary and sufficient conditions for quadratic stabilizability of an uncertain system. J. Optimization Theory and Applications, 46(4), Aug. 1985. D. Peaucelle, D. Arzelier, O. Bachelier, and J. Bernussou. A new robust D-stability condition for real convex polytopic uncertainty. Systems & Control Letters, 40(1):21–30, May 2000.

Course outcomes: 1. 2. 3. 4. 5. 6. 7. 8.

Synthesize of uncertain linear systems in continuous time and discrete time. Define, isolate, and formalize the system uncertainties. Learn how to add more control objectives and get a possible solution. Design, assess, and simulate linear robust feedback under system uncertainties. Construct, demonstrate, analyze, synthesize, and implement robust feedback under system uncertainties. Assess and apply modern optimal and robust 𝐻2 and 𝐻∞ feedbacks. Understand the difference between robust and adaptive control. Learn how to solve multi-objective control problems.

Grading Policy: Home-works: 15% Project: 25% Mid-Term Exam: 25% Final Exam: 35%

Tentative schedule Week

Topics

1

January 6th

2

January 13th

3

January 20th

4

January 27th

5

February 3rd

6

February

10th

7

February 17th

8

February 24th

9

March 3rd

10

11

12

March 10th

March 17th March 24th

Signal norms, Different norms of transfer function, Positive-definite matrices and their properties, The Algebraic Ricatti Equation (ARE), State-space modeling, Lyapunov function, exponential stability. Different types of system uncertainty, Modeling of uncertain linear systems, External uncertainties, Systems with uncertain parameters, Controlling under system uncertainty conditions. Norm-bounded uncertainties, polytopic uncertainties, 𝐻2 and 𝐻∞norms of transfer functions, SISO and MIMO systems. Stability of uncertain continuous-time linear systems, stabilizability of linear continuous-time systems. Linear Matrix Inequalities (LMIs) in Control, Convex optimization, The search of possible numerical solutions, LMIs versus AREs. Stability of discrete-time uncertain systems, stabilizability issues, Limitation of linear state-space feedbacks. Prescribed degree of stability, optimal pole placement, LMI characterization Presentation and utilization of the convex-optimization routines of Matlab, case studies. 𝐻∞ Control of linear systems, Design examples, Numerical simulations. The continuous time case 𝐻∞ Control of linear systems, Design examples, Numerical simulations. The discrete-time case. 𝐻2 Control of linear systems, Design examples, Numerical simulations. The continuous time and the discrete-time cases. Mixed 𝐻2 -𝐻∞ control objective. The continuous-time and the discrete time cases

Reading Assignment

Assignments and Projects

Lecturer Notes 1

Lecturer Notes 2

Homework 1 Projects distribution and selection

Lecturer Notes 3

Deadline of project selection

Lecturer Notes 3

Homework 1 due by the end of week 4.

Lecturer Notes 4

Homework 2

Lecturer Notes 5

First progress reports of the projects are due (Literature Review must be completed by the end of week 6)

Lecturer Notes 6 Simulation

Homework 2 is due by the end of week 8 Distribution of Homework 3

Lecturer Notes 7 Lecturer Notes 7 Lecturer Notes 8 Lectures notes 9

Major Exam Homework 3 is due by the end of week 13 Projects due by the end of week 13. Final report must be submitted as hard copy. Strict deadline

13

March 31st

𝐻∞ filtering, tracking, domain stability, and multi-objective control design, LMI formulations, Case studies

14

April 7th

Project presentations and discussions. Oral presentations followed by questions.

Lecturer Notes 10

15

April 14h

Review session

Lecturer Notes 11

April 18th, 2019: Last day of classes Final examination period: April 20th to May 1st 2019 Final Exam: Refer to the registrar web site

Important point to remember Pre-requisite: Upon entering this course, all the students should be able to: ✓ Demonstrate a good understanding of the fundamental theory of linear systems in continuous-time and discrete time; ✓ Demonstrate basic understanding of system stability theory in state space; ✓ Demonstrate a good knowledge of differential equations and basic notions of linear algebra; ✓ Perform numerical simulations using Matlab/Simulink software. Projects: One or two students can select one common project. All the projects may cover one or more topics in system design and control. The project cannot be changed after selection. Academic dishonesty is a serious offense which should not be taken lightly. Cheating, falsification, and plagiarism are both forms of academic dishonesty. Please note that academic dishonesty has grave consequences which may include receiving “no grade” on the project. Attendance: According to the university regulations, any student that exceeds 20% (9 lectures) of the scheduled class meeting without an official excuse will receive a grade DN in the course. Official excuses: All official excuses must be submitted to the instructor no later than one week of the date of the official excuse. The instructor may not accept late excuses. Lecturer notes: The lecturer notes that are distributed in class or sent as electronic files are supporting documents that enhance the content or clarify the difficult aspects of the course. The lecturer notes can be also the electronic files of the slides discussed in course.