# UBC Math 403—Sep–Dec 2012

The most recent additions to this list of resources appear at the top. See the Draft Course Outline for policies and contact information.

 Code Due Details Last Change EXAM Final Examination Review Here is a copy of the 2012 final exam, lightly edited for cosmetics. Some students will also be interested in the solutions. 19 Dec 2012 EXAM Final Examination Notes Unofficially, our exam runs from 12:00–14:30 on Wednesday 12 December, in room MATH 102. To be really certain of these details, check the official exam schedule. For the final examination, students may bring and use anything written in their own hand, and printed copies of any materials from the course web page. That's a complete list. All electronic resources are banned; all paper documents not mentioned above are also forbidden. Some past final exams from earlier years are here: 2003, 2004, 2006, 2010. 03 Dec 2012 RR Stability of Equilibria The Liapunov Stability Theory has a simple basic idea, but repays further study and reflection. It's our final topic for this term. 24 Nov 2012 HW 30 Nov 2012 Assignment 9 The first two of these five exercises use Dynamic Programming; in one of them the details from the online notes can save a lot of work. Posted after the due date: complete solutions. GOOD NEWS: All submissions are marked and ready for pickup from the box just outside the instructor's door. 07 Dec 2012 RR Dynamic Programming These recent notes on Dynamic Programming are pretty “drafty”: comments and corrections from readers would be most welcome! (One of the detailed examples should be useful on Assignment 9.) 24 Nov 2012 HW 21 Nov 2012 Assignment 8 Two of the next three exercises are direct applications of the maximum principle; the third relies on the model problem discussed in class. Posted after the due date: complete solutions. 16 Nov 2012 RR Fishing and Related Topics Here are some notes on Optimal Fishing: Velocity Constraints, Discounting, Singular Arcs that are a little more polished than the version presented in class over the last few days. 16 Nov 2012 HW 14 Nov 2012 Assignment 7 The next five exercises are all applications of the maximum principle. Some involve constraints on the final state. Posted after the due date: complete solutions. 07 Nov 2012 RR Helpful Online Resources Professor L. C. Evans of Berkeley has excellent notes online: An Introduction to Mathematical Optimal Control Theory, Version 0.2. They include some classic examples we may not have time to see in class. 07 Nov 2012 RR The Maximum Principle Here is a tidy summary statement of the Pontryagin Maximum Principle for a rather general collection of optimal control problems. 07 Nov 2012 HW 07 Nov 2012 Assignment 6 Here are four questions involving LTI systems. (The rocket car shows up in disguise a couple of times.) Posted after the due date: complete solutions. 31 Oct 2012 RR Another Example Here is a cleaned-up version of today's lecture notes on a fixed-time problem with rocket-car dynamics, including a precise computer-generated illustration. 24 Oct 2012 HW 29 Oct 2012 Assignment 5 Here are four questions involving extremality, attainable sets, and the minimum-time problem for LTI systems. (Some of the solutions will span several pages!) The Matlab script rocketspring.m may help with Question 3, under the conditions described in class. Posted after the due date: complete solutions. 01 Nov 2012 RR Extended Example The Rocket Car 22 Oct 2012 EXAM 19 Oct 2012 Midterm Exam The test had three questions involving linearization, stability, controllability, linear feedback, and convexity. Posted well after the test (then edited on 02 Nov): complete solutions. 02 Nov 2012 HW 15 Oct 2012 Assignment 4 Here are five questions involving observability, observer design, and convexity. Posted after the due date: complete solutions. 05 Oct 2012 RR Lecture Support Pole Placement Example: Response Plots for Three Choices; Matlab script 28 Sep 2012 HW 01 Oct 2012 Assignment 3 Here are six questions involving linearization, controllability, and related topics. Posted after the due date: complete solutions. 25 Sep 2012 RR Lecture Notes Chapter II: Control of Autonomous Linear Systems 19 Sep 2012 HW 24 Sep 2012 Assignment 2 Here are five questions involving systems of linear differential equations, the last of which involves control. Edit: Changed due date to Monday 24 Sep. Posted after the due date: complete solutions. 20 Sep 2012 HW 14 Sep 2012 Assignment 1 Here are four questions on systems of linear differential equations. The methods on pages 4–11 of the posted lecture notes on Controlled ODE's should be powerful enough to solve them. Posted after the due date: complete solutions. 07 Sep 2012 RR Lecture Notes Chapter I: Controlled Ordinary Differential Equations 05 Sep 2012 RR Course Outline for Autumn 2012 — Topic list still negotiable! 05 Sep 2012 RR Professor Loewen's Home Page 05 Sep 2012

Codes: RR = reading/reference; PP = practice problems (not to hand in); HW = homework problems (to be submitted); EXAM = midterm or final exam materials.

Last update: 19 Dec 2012 (Wed), 23:00:14. (Click a graphic to recheck.)