SE PhD Prospectus Defense of Julia Lima Fleck

TITLE: Perturbation Analysis in Stochastic Hybrid Systems: Applications to Transportation Systems and Systems Biology ABSTRACT: The first part of this work addresses the Traffic Light Control (TLC) problem for a single intersection modeled as a Stochastic Hybrid System (SHS). A quasi-dynamic control policy is proposed based on partial state information defined by detecting whether vehicle backlogs are above or below certain controllable threshold values. At first, the threshold parameters are controlled while assuming fixed cycle lengths and online gradient estimates of a cost metric with respect to these controllable parameters are derived using Infinitesimal Perturbation Analysis (IPA) techniques. These estimators are subsequently used to iteratively adjust the threshold values so as to improve overall system performance. This quasidynamic analysis of the TLC problem is subsequently extended to parameterize the control policy by green and red cycle lengths as well as queue content thresholds. IPA estimators necessary to simultaneously control the light cycles and thresholds are rederived and thereafter incorporated into a gradient-based scheme in order to further ameliorate system performance. In the second part of this work, the problem of controlling cancer progression is formulated within a Stochastic Hybrid Automaton (SHA) framework. Leveraging the fact that cell-biologic changes necessary for cancer development may be schematized as a series of discrete steps, and that transitions between such steps may be delayed or prevented by appropriate treatment, a novel SHA representation of tumor evolution is proposed. A methodology is outlined for using IPA to determine optimal cancer treatments so as to tailor therapies based on the characteristics of a given tumor. The goal of this ongoing work is to construct a Discrete Event System (DES) simulation environment suited for analyzing the effect of different treatment protocols on the progression of cancer. A description is given of future steps necessary to develop a method for estimating the sensitivity of a therapy’s performance to a set of chosen controllable system parameters, whose values can then be subsequently optimized. COMMITTEE: Advisor: Christos Cassandras, SE/ECE; Ioannis Paschalidis, SE/ECE; Calin Belta, SE/ME; Mac Schwager, SE/ME