Warren J. Code

My MSc work concerned Sturn-Liouville problems where the eigenparameter appears in one of the boundary conditions; this can occurs in, for example, modeling wave propagation across a boundary connecting two media. Some favourite tools in approaching this type of problem include the clever transformation due to Prüfer as well a technique adapted from work of Crum and Darboux to convert into equivalent standard Sturm-Liouville problems. My supervisor was Patrick Browne at the University of Saskatchewan; I graduated in October, 2003.

I shifted fields a bit for my PhD, where I learned nonsmooth analysis and its application to optimal control (in the state space setting). My thesis work involved impulsive systems, used in models with two dramatically different timescales such that one is treated as a discrete action (the faster time scale) and the other as continuous flow (the slower time sclae). One way analysis can proceed is by "stretching out" the discrete jump events using an alternate timescale choice. I considered applications of this methos in stabilization problems as well as necessary conditions for optimal control under fairly loose hypotheses in nonlinear control. My supervisor was Philip Loewen at the University of British Columbia; I completed my program in December, 2009.

Code, Warren J.; Loewen, Philip D.
Optimal control of non-convex measure-driven differential inclusions.
Set-Valued and Variational Analysis: Volume 19, Issue 2 (2011), Page 203. Electronic version here.

Code, Warren J.; Silva, Geraldo N.
Closed loop stability of measure-driven impulsive control systems.
Journal of Dynamical and Control Systems. 16 (2010), no. 1, 1--21.

Code, Warren J.
Measure-Driven Impulsive Systems: Stabilization, Optimal Control and Applications.
University of British Columbia, PhD Thesis (2009). Permanent URL: http://hdl.handle.net/2429/17450

Code, Warren J.; Silva, Geraldo N.
Stabilization of certain control-affine measure-driven impulsive control systems.
International Journal of Mathematics and Statistics. 5 (2009), no. A09, Special Issue Generalized Differentiation, Variational Analysis and Mathematical Control Theory -- a 60th Birthday Tribute to Boris S. Mordukhovich.

Code, Warren J.; Browne, Patrick J.
Sturm-Liouville problems with boundary conditions depending quadratically on the eigenparameter.
Journal of Mathematical Analysis and Applications. 309 (2005), no. 2, 729--742.

Binding, Paul A.; Browne, Patrick J.; Code, Warren J.; Watson, Bruce A.
Transformation of Sturm-Liouville problems with decreasing affine boundary conditions.
Proceedings of the Edinburgh Mathematical Society. 47 (2004), no. 3, 533--552.

Code, Warren J.
Sturm-Liouville Problems with Eigenparameter-Dependent Boundary Conditions
University of Saskatchewan, MSc Thesis (2003).

Code, Warren J.; Taylor, Keith F.
Farey Sequences. An online presentation of a mathematical applet (mathlet).
Submitted.

CONTROLO 2008, Stabilization of certain control-affine measure-driven impulsive control systems. (Joint work with Geraldo N. Silva.) July 2008, Vila Real, Portugal.

West Coast Optimization Fall Meeting, Closed loop stability of measure-driven impulsive systems. October 2007, Kelowna, BC.

UBC Mathematics Graduate Student Seminar:

• Impulsive differential equations via measures. March 2008.
• Introduction to control theory. November 2007.
• Introduction to Sturm-Liouville theory. September 2006.

University of Saskatchewan Math & Stats Department Seminar, Sturm-Liouville Problems with an eigenparameter in the boundary conditions. March 2003.