Topic Outline (Highly Negotiable!)
Differential Equations, Invariance, Stability
 Linear constantcoefficient equations
 Linear variablecoefficient ODE's
 Nonlinear ODE's
 Controlled ODE's
 Linearization
 Examples

9 
Linear Control Systems
 Controllability
 Eigenvalue assignment by state feedback
 Control constraints; Attainable Sets
 Geometry of R^{n}
 Boundary Trajectories
 TimeOptimal Control
 Examples: Rocket Car, Harmonic Oscillator
 Unconstrained problems with quadratic objectives

10 
LinearQuadratic Optimal Control
 Openloop versus feedback formulations
 Geometric Approach
 Dynamic Programming Approach
 Responseshaping by coefficient selection
 Robust stability of LQ designs (but no Hinfinity
material)

5 
Nonlinear Optimal Control
 Freeterminalpoint problems
 Pontryagin Maximum Principle
 Problems linear in the control; singular arcs
 Turnpike solutions

6 
Recent Advances
One topic of current research interest selected by the
instructor in consultation with the class, e.g.,
 Lyapunov's Direct Method, Flowinvariant sets, LaSalle's Theorem
 InfiniteHorizon problems
 RecedingHorizon Control
 HamiltonJacobi Theory
 Hinfinity
 Linear Matrix Inequalities in control system design

4 
Total lecturehours (excluding test) 
35 
DetailsAutumn 2012
Required Text:
 None. Lecture notes will be provided.
Class Test:
19 Oct (Fri), 13:0013:50 (50 minutes).
Other Important Dates:
 05 Sep (Wed): Lecture 1—the first of the term.
 18 Sep (Tue): Deadline to withdraw without having “W” appear on record.
 12 Oct (Fri): Deadline to withdraw.
 19 Oct (Fri): Midterm in class.
 30 Nov (Fri): Last class of the term.
 12 Dec (Wed): Final Examination, 12:00, room MATH 102.
[Unofficial; here is the
official exam schedule.]
Grading Formula:
You can earn up to 40% from Homework due each Friday; 10% from
the midterm test; and 50% from the Final Examination. The exam will
last 2.5 hours, and be held at some time during UBC's formal
examination period. The homework will be challenging and essential.
Grades may be scaled due to the challenging nature of the course
material.
Policies:
 There is no supplemental examination in this course.
 Late homework assignments receive a grade of 0.
 Missing a midterm normally results in a mark of 0. Exceptions
may be granted in two cases: prior consent of the instructor or a
medical emergency. In the latter case, the instructor must be
notified within 48 hours of the missed test, and presented with a
doctor's note immediately upon the student's return to UBC.
Dr. Philip D. Loewen
Office: 
Mathematics Building, room 207 
Email: 
loew@math.ubc.ca
(try this first) 
Office phone: 
6048223082 (urgent cases only, please) 
URI: 
https://personal.math.ubc.ca/~loew/

Official Calendar Entry
MATH 403 (3)
Stabilization and Optimal Control of Dynamical Systems.
Dynamical systems; stability by Liapunov's direct method;
controllability and eigenvalue assignment for autonomous linear systems;
linearquadratic regulator, time optimal control, Pontryagin maximum
principle, dynamic programming; applications in engineering, economics
and resource management.
Prerequisite: 1 of MATH 320, MATH 301. A grade of at least 68% in
either course is required. MATH 402 is recommended. [300]
Last update: 25 Jul 2022 (Mon), 12:27:27.
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