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Topics in perturbation analysis for stochastic hybrid systems

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Control and optimization of Stochastic Hybrid Systems SHS constituteincreasingly active fields of research. However, the size and complexity ofSHS frequently render the use of exhaustive verification techniquesprohibitive. In this context, Perturbation Analysis techniques, and inparticular Infinitesimal Perturbation Analysis IPA, have proven to beparticularly useful for this class of systems. This work focuses on applyingIPA to two different problems: Traffic Light Control TLC and control ofcancer progression, both of which are viewed as dynamic optimizationproblems in an SHS environment.The first part of this thesis addresses the TLC problem for a singleintersection modeled as a SHS. A quasi-dynamic control policy is proposedbased on partial state information defined by detecting whether vehiclebacklogs are above or below certain controllable threshold values. At first,the threshold parameters are controlled while assuming fixed cycle lengthsand online gradient estimates of a cost metric with respect to thesecontrollable parameters are derived using IPA techniques. These estimatorsare subsequently used to iteratively adjust the threshold values so as toimprove overall system performance. This quasi-dynamic analysis of the TLC\problem is subsequently extended to parameterize the control policy by greenand red cycle lengths as well as queue content thresholds. IPA estimatorsnecessary to simultaneously control the light cycles and thresholdsare rederived and thereafter incorporated into a standard gradient basedscheme in order to further ameliorate system performance.In the second part of this thesis, the problem of controlling cancerprogression is formulated within a Stochastic Hybrid Automaton SHAframework. Leveraging the fact that cell-biologic changes necessary for cancer development may be schematized as a series of discrete steps, an integrative closed-loop framework is proposed for describing the progressive development of cancer and determining optimal personalized therapies. First, the problem of cancer heterogeneity is addressed through a novel Mixed Integer Linear Programming MILP formulation that integrates somatic mutation and gene expression data to infer the temporal sequence of events from cross-sectional data. This formulation is tested using both simulated data and real breast cancer data with matched somatic mutation and gene expression measurements from The Cancer Genome Atlas TCGA. Second, the use of basic IPA techniques for optimal personalized cancer therapy design is introduced and a methodology applicable to stochastic models of cancer progression is developed. A case study of optimal therapy design for advanced prostate cancer is performed. Given the importance of accurate modeling in conjunction with optimal therapy design, an ensuing analysis is performed in which sensitivity estimates with respect to several model parameters are evaluated and critical parameters are identified. Finally, the tradeoff between system optimality and robustness or, equivalently, fragility is explored so as to generate valuable insights on modeling and control of cancer progression.

Boston University Theses and Dissertations -

Autor: Lima Fleck, Julia - -



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