Jeffrey D. Azzato

A parallel Matlab package for approximating the solution to a continuous-time stochastic optimal control problem

Computing the solution to a stochastic optimal control problem is difficult. A method of approximating a solution to a given stochatic optimal problem was developed in [1]. This paper describes a suite of Matlab functions implementing this method of approximating a solution to a given continuous stochastic optimal control problem.

Applying a finite-horizon numerical optimization method to a periodic optimal control problem

Computing a numerical solution to a periodic optimal control problem can be difficult, especially when the period is unknown. A method of approximating a solution to a stochastic optimal control problem using Markov chains was developed in [Krawczyk, J. B. (2001). A Markovian approximated solution to a portfolio management problem. Information Technology for Economics and Management, 1, http://www.item.woiz.polsl.pl/issue/journal1.htm]. This paper describes the application of that method to a periodic optimal control problem formulated in [Gaitsgory, V. & Rossomakhine, S. (2006). Linear programming approach to deterministic long run average problems of optimal control. SIAM Journal on Control and Optimization, 44(6), 2006-2037]. As a result, approximately optimal feedback rules are computed that can control the system both on and off the optimal orbit.

Linked tree-decompositions of represented infinite matroids

We prove that a represented infinite matroid having finite tree-width w has a linked tree-decomposition of width at most 2w. This result should be a key lemma in showing that any class of infinite matroids representable over a fixed finite field and having bounded tree-width is well-quasi-ordered under taking minors. We also show that for every finite w, a represented infinite matroid has tree-width at most w if and only if all its finite submatroids have tree-width at most w. Both proofs rely on the use of a notion of chordality for represented matroids.