Topics in perturbation analysis for stochastic hybrid systems

Control and optimization of Stochastic Hybrid Systems (SHS) constitute increasingly active fields of research. However, the size and complexity of SHS frequently render the use of exhaustive verification techniques prohibitive. In this context, Perturbation Analysis techniques, and in particular Infinitesimal Perturbation Analysis (IPA), have proven to be particularly useful for this class of systems. This work focuses on applying IPA to two different problems: Traffic Light Control (TLC) and control of cancer progression, both of which are viewed as dynamic optimization problems in an SHS environment. The first part of this thesis addresses the TLC problem for a single intersection modeled as a 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 IPA techniques. These estimators are subsequently used to iteratively adjust the threshold values so as to improve overall system performance. This quasi-dynamic 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 standard gradient based scheme in order to further ameliorate system performance. In the second part of this thesis, 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, 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

Simulation optimization: A comprehensive review on theory and applications

For several decades, simulation has been used as a descriptive tool by the operations research community in the modeling and analysis of a wide variety of complex real systems. With recent developments in simulation optimization and advances in computing technology, it now becomes feasible to use simulation as a prescriptive tool in decision support systems. In this paper, we present a comprehensive survey on techniques for simulation optimization with emphasis given on recent developments. We classify the existing techniques according to problem characteristics such as shape of the response surface (global as compared to local optimization), objective functions (single or multiple objectives) and parameter spaces (discrete or continuous parameters). We discuss the major advantages and possible drawbacks of the different techniques. A comprehensive bibliography and future research directions are also provided in the paper. © "IIE"

Control and optimization methods for problems in intelligent transportation systems

This thesis aims to address three research topics in intelligent transportation systems which include multi-intersection traffic light control based on stochastic flow models with delays and blocking, optimization of mobility-on-demand systems using event-driven receding horizon control and the optimal control of lane change maneuvers in highways for connected and automated vehicles. First, for the traffic light control work, we extend Stochastic Flow Models (SFMs), used for a large class of discrete event and hybrid systems, by including the delays which typically arise in flow movements, as well as blocking effects due to space constraints. We apply this framework to the multi-intersection traffic light control problem by including transit delays for vehicles moving from one intersection to the next and possible blocking between two intersections. Using Infinitesimal Perturbation Analysis (IPA) for this SFM with delays and possible blocking, we derive new on-line gradient estimates of several congestion cost metrics with respect to the controllable green and red cycle lengths. The IPA estimators are used to iteratively adjust light cycle lengths to improve performance and, in conjunction with a standard gradient-based algorithm, to obtain optimal values which adapt to changing traffic conditions. The second problem relates to developing an event-driven Receding Horizon Control (RHC) scheme for a Mobility-on-Demand System (MoDS) in a transportation network where vehicles may be shared to pick up and drop off passengers so as to minimize a weighted sum of passenger waiting and traveling times. Viewed as a discrete event system, the event-driven nature of the controller significantly reduces the complexity of the vehicle assignment problem, thus enabling its real-time implementation. Finally, optimal control policies are derived for a Connected Automated Vehicle (CAV) cooperating with neighboring CAVs in order to implement a lane change maneuver consisting of a longitudinal phase where the CAV properly positions itself relative to the cooperating neighbors and a lateral phase where it safely changes lanes. For the first phase, the maneuver time subject to safety constraints and subsequently the associated energy consumption of all cooperating vehicles in this maneuver are optimized. For the second phase, time and energy are jointly optimized based on three different solution methods including a real-time approach based on Control Barrier Functions (CBFs). Structural properties of the optimal policies which simplify the solution derivations are provided in the case of the longitudinal maneuver, leading to analytical optimal control expressions. The solutions, when they exist, are guaranteed to satisfy safety constraints for all vehicles involved in the maneuver

Contributions to shared control and coordination of single and multiple robots

L’ensemble des travaux présentés dans cette habilitation traite de l'interface entre un d'un opérateur humain avec un ou plusieurs robots semi-autonomes aussi connu comme le problème du « contrôle partagé ».Le premier chapitre traite de la possibilité de fournir des repères visuels / vestibulaires à un opérateur humain pour la commande à distance de robots mobiles.Le second chapitre aborde le problème, plus classique, de la mise à disposition à l’opérateur d’indices visuels ou de retour haptique pour la commande d’un ou plusieurs robots mobiles (en particulier pour les drones quadri-rotors).Le troisième chapitre se concentre sur certains des défis algorithmiques rencontrés lors de l'élaboration de techniques de coordination multi-robots.Le quatrième chapitre introduit une nouvelle conception mécanique pour un drone quadrirotor sur-actionné avec pour objectif de pouvoir, à terme, avoir 6 degrés de liberté sur une plateforme quadrirotor classique (mais sous-actionné).Enfin, le cinquième chapitre présente une cadre général pour la vision active permettant, en optimisant les mouvements de la caméra, l’optimisation en ligne des performances (en terme de vitesse de convergence et de précision finale) de processus d’estimation « basés vision »

Quantitative Techniques in Participatory Forest Management

Forest management has evolved from a mercantilist view to a multi-functional one that integrates economic, social, and ecological aspects. However, the issue of sustainability is not yet resolved. Quantitative Techniques in Participatory Forest Management brings together global research in three areas of application: inventory of the forest variables that determine the main environmental indices, description and design of new environmental indices, and the application of sustainability indices for regional implementations. All these quantitative techniques create the basis for the development of scientific methodologies of participatory sustainable forest management

Quantitative Techniques in Participatory Forest Management

Forest management has evolved from a mercantilist view to a multi-functional one that integrates economic, social, and ecological aspects. However, the issue of sustainability is not yet resolved. Quantitative Techniques in Participatory Forest Management brings together global research in three areas of application: inventory of the forest variables that determine the main environmental indices, description and design of new environmental indices, and the application of sustainability indices for regional implementations. All these quantitative techniques create the basis for the development of scientific methodologies of participatory sustainable forest management

AN EXAMINATION OF MULTIPLE OPTIMIZATION APPROACHES TO THE SCHEDULING OF MULTI-PERIOD MIXED-BTU NATURAL GAS PRODUCTS

As worldwide production and consumption of natural gas increase, so does the importance of maximizing profit when trading this commodity in a highly competitive market. Decisions regarding the buying, storing and selling of natural gas are difficult in the face of high volatility of prices and uncertain demand. With the introduction of alternative sources of fuels with lower levels of methane, the primary component of natural gas, these decisions become more complicated. This is an issue faced by investors as well as operational planners of industrial and commercial consumers of natural gas where incorrect planning decisions can be costly.A great deal of research in the academic and commercial arenas has been accomplished regarding the problem of optimizing the scheduling of injection and withdrawal of this commodity. While various commercial products have been in use for years and research on new approaches continues, one aspect of the problem that has received less attention is that of combining gases of different heat contents. This study examines multiple approaches to maximizing profits by optimally scheduling the purchase and storage of two gas products of different energy densities and the sales of the same in combination with a product that is a blend of the two. The result provides an initial basis for planners to improve decision making and minimize the cost of natural gas consumed.This multi-product multi-period finite (twelve-month) horizon product-mix problem is NP-Hard. The first approach developed is a Branch and Bound (B&B) technique combined with a linear program (LP) solver. Heuristics are applied to limit the expansion the trinomial tree generated. In the second approach, a stochastic search algorithm-linear programming hybrid (SS-LP) is developed. The third approach implemented is a pure random search (PRS). To make each technique computationally tractable, constraints on the units of product moved in each transaction are implemented.Then, using numerical data, the three approaches are tested, analyzed and compared statistically and graphically along with computer performance information. The best approach provides a tool for optimizing profits and offers planners an advantage over approaches that are solely history-based