UBC Math 403, Autumn 2012
MWF 13:00-13:50, room MATH 204

Topic Outline (Highly Negotiable!)

Topic Hours
Differential Equations, Invariance, Stability
  • Linear constant-coefficient equations
  • Linear variable-coefficient ODE's
  • Nonlinear ODE's
  • Controlled ODE's
  • Linearization
  • Examples
Linear Control Systems
  • Controllability
  • Eigenvalue assignment by state feedback
  • Control constraints; Attainable Sets
  • Geometry of Rn
  • Boundary Trajectories
  • Time-Optimal Control
  • Examples: Rocket Car, Harmonic Oscillator
  • Unconstrained problems with quadratic objectives
Linear-Quadratic Optimal Control
  • Open-loop versus feedback formulations
  • Geometric Approach
  • Dynamic Programming Approach
  • Response-shaping by coefficient selection
  • Robust stability of LQ designs (but no H-infinity material)
Nonlinear Optimal Control
  • Free-terminal-point problems
  • Pontryagin Maximum Principle
  • Problems linear in the control; singular arcs
  • Turnpike solutions
Recent Advances

One topic of current research interest selected by the instructor in consultation with the class, e.g.,

  • Lyapunov's Direct Method, Flow-invariant sets, LaSalle's Theorem
  • Infinite-Horizon problems
  • Receding-Horizon Control
  • Hamilton-Jacobi Theory
  • H-infinity
  • Linear Matrix Inequalities in control system design
Total lecture-hours (excluding test) 35

Details--Autumn 2012

Required Text:

Class Test:

19 Oct (Fri), 13:00-13:50 (50 minutes).

Other Important Dates:

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.



Dr. Philip D. Loewen

Office:  Mathematics Building, room 207
Email:  loew@math.ubc.ca (try this first)
Office phone:  604-822-3082 (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; linear-quadratic 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. [3-0-0]

Last update: 25 Jul 2022 (Mon), 12:27:27.

Valid XHTML 1.0! Valid CSS! (Click a graphic to recheck.)