CS 412: Linear Programming and Convex Optimzation
Professor Sean Warnick
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
The following is BYU's statement on preventing sexual harassment:
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.