CS 412: Linear Programming and Convex Optimzation

Course Description

Design of algorithms to make decisions in complex, uncertain environment.

Text

MIT OCW 6.241, 6.245
"A Course in Robust Control Theory," by Dullerud and Paganini
"Feedback Control Theory," by Doyle, Francis, and Tannenbaum
Supplemental text:
"Feedback Systems: An Introduction for Scientists and Engineers," by Astrom and Murray

Typical Schedule

Week 1		Reading	Assigned	Due
Th	Course overview, introduction to dynamical systems and control
Week 2		Reading	Assigned	Due
T	Linear Algebra Review	6.241 Chapter 1	HW 1
Th	Linear Algebra Review	6.241 Chapter 1
Week 3		Reading	Assigned	Due
T	Least squares (overdetermined systems)	6.241 Chapter 2	HW 2	HW 1
Th	Least squares (underdetermined systems)	6.241 Chapter 3
Week 4		Reading	Assigned	Due
T	Matrix norms, SVD	6.241 Chapter 4	HW 3	HW 2
Th	Matrix perturbations	6.241 Chapter 5
Week 5		Reading	Assigned	Due
T	State space models	6.241 Chapters 6, 7, 8; Astrom & Murray Chapters 4, 5	HW 4	HW 3
Th	Solutions of state space models	6.241 Chapters 10-11; Astrom & Murray Chapters 4, 5
Week 6		Reading	Assigned	Due
T	Similarity transformations, modes of LTI systems, Laplace transform, transfer functions	6.241 Chapter 12; Astrom & Murray Chapter 8	HW 5	HW 4
Th	Stability, Lyapounov methods	6.241 Chapters 13, 14
Week 7		Reading	Assigned	Due
T	External I/O stability, storage functions	6.241 Chapter 15	HW 6	HW 5
Th	Interconnected systems, I/O stability	6.241 Chapter 17
Week 8		Reading	Assigned	Due
T	No Class		HW 7
Th	System norms	6.241 Chapter 16		HW 6
Week 9		Reading	Assigned	Due
T	Performance measure in feedback control	6.241 Chapter 18	HW 8	HW 7
Th	Small gain theorem, stability robustness	6.241 Chapter 19
Week 10		Reading	Assigned	Due
T	MIMO stability robustness	6.241 Chapters 20, 21	HW 9	HW 8
Th	Reachability	6.241 Chapter 22
Week 11		Reading	Assigned	Due
T	Reachability: standard and canonical forms, modal tests	6.241 Chapter 23	HW 10	HW 9
Th	Observability	6.241 Chapter 24
Week 12		Reading	Assigned	Due
T	Minimality, realization, Kalman decomposition, model reduction	6.241 Chapter 25	HW 11	HW 10
Th	State feedback, observers, ouput feedback, MIMO poles and zeros	6.241 Chapters 26, 27, 28, 29
Week 13		Reading	Assigned	Due
T	Minimality of interconnections, pole/zero cancellations	6.241 Chapter 30	TBD	HW 11
Th	Parameterization of all stabilizing controllers	Dullerud and Paganini
Week 14		Reading	Assigned	Due
T	Optimal control synthesis: problem setup	Dullerud and Paganini	TBD	TBD
Th	H2 Optimization	Dullerud and Paganini
Week 14		Reading	Assigned	Due
T	H∞ Optimization	Dullerud and Paganini		TBD
Th	Reading Day - No Class

Grades

Grades are by the following distribution and scale:

• Homework 50%
• Project 25%
• Final Exam 25%

100-93 A	93-90 A-	90-87 B+
87-83 B	83-80 B-	90-77 C+
77-73 C	73-70 C-	70-67 D+
67-63 D	63-60 D-	60-0 E

We reserve the right to curve grades in your favor. The University policies on UW and I grades will be strictly followed.

Harrassment

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Title IX of the Education Amendments of 1972 prohibits sex discrimination against any participant in an educational program or activity receiving federal funds. The act is intended to eliminate sex discrimination in education. Title IX covers discrimination in programs, admissions, activities, and student-to-student sexual harassment. BYU's policy against sexual harassment extends not only to employees of the university but to students as well. If you encounter unlawful sexual harassment or gender based discrimination, please talk to your professor; contact the Equal Employment Office at 378-5895 or 367-5689 (24 hours); or contact the Honor Code Office at 378-2847.