Decentralized control of compartmental networks with H∞ tracking performance

published_or_final_versio

Control and optimization algorithms for air transportation systems

Modern air transportation systems are complex cyber-physical networks that are critical to global travel and commerce. As the demand for air transport has grown, so have congestion, flight delays, and the resultant environmental impacts. With further growth in demand expected, we need new control techniques, and perhaps even redesign of some parts of the system, in order to prevent cascading delays and excessive pollution. In this survey, we consider examples of how we can develop control and optimization algorithms for air transportation systems that are grounded in real-world data, implement them, and test them in both simulations and in field trials. These algorithms help us address several challenges, including resource allocation with multiple stakeholders, robustness in the presence of operational uncertainties, and developing decision-support tools that account for human operators and their behavior. Keywords: Air transportation; Congestion control; Large-scale optimization; Data-driven modeling; Human decision processe

Feedback Control of the National Airspace System

This paper proposes a general modeling framework adapted to the feedback control of traffic flows in Eulerian models of the National Airspace System. It is shown that the problems of scheduling and routing aircraft flows in the National Airspace System can be posed as the control of a network of queues with load-dependent service rates. Focus can then shift to developing techniques to ensure that the aircraft queues in each airspace sector, which are an indicator of the air traffic controller workloads, are kept small. This paper uses the proposed framework to develop control laws that help prepare the National Airspace System for fast recovery from a weather event, given a probabilistic forecast of capacities. In particular, the model includes the management of airport arrivals and departures subject to runway capacity constraints, which are highly sensitive to weather disruptions.National Science Foundation (U.S.) (Contract ECCS-0745237)United States. National Aeronautics and Space Administration (Contract NNA06CN24A

Numerical Simulation

Nowadays mathematical modeling and numerical simulations play an important role in life and natural science. Numerous researchers are working in developing different methods and techniques to help understand the behavior of very complex systems, from the brain activity with real importance in medicine to the turbulent flows with important applications in physics and engineering. This book presents an overview of some models, methods, and numerical computations that are useful for the applied research scientists and mathematicians, fluid tech engineers, and postgraduate students

Control Problems for Conservation Laws with Traffic Applications

Conservation and balance laws on networks have been the subject of much research interest given their wide range of applications to real-world processes, particularly traffic flow. This open access monograph is the first to investigate different types of control problems for conservation laws that arise in the modeling of vehicular traffic. Four types of control problems are discussed - boundary, decentralized, distributed, and Lagrangian control - corresponding to, respectively, entrance points and tolls, traffic signals at junctions, variable speed limits, and the use of autonomy and communication. Because conservation laws are strictly connected to Hamilton-Jacobi equations, control of the latter is also considered. An appendix reviewing the general theory of initial-boundary value problems for balance laws is included, as well as an appendix illustrating the main concepts in the theory of conservation laws on networks

Local to Global Multi-Scale Multimedia Modeling of Chemical Fate and Population Exposure

To assess environmental and human exposure to chemical emissions, two types of approaches are available: 1. intermediate- to high-resolution, substance/location-specific analyses, and 2. lower resolution, less specific analyses aiming for broad coverage. The first category is time/resource intensive, which limits its utility, while the second is less accurate but allows for evaluation of large numbers of substances/situations. None is well suited for analyzing local to global population exposure. We need a multi-scale approach of intermediate complexity that bridges the advantages of both approaches: high resolution when relevant, the ability to evaluate large numbers of substances, and a level of accuracy that is “useful” (for decision-makers). This thesis aims to 1. develop a multi-scale, multimedia fate and transport, and multi-pathway population exposure modeling framework, 2. evaluate it using large-scale inventories of emissions and measured environmental concentrations, 3. evaluate local to global population exposure associated with large sets of point sources covering a wide variety of local contexts (e.g. up/down-wind/stream from large populations, important water bodies or agricultural resources), and 4. simulate a large national inventory of emissions and perform multi-media source apportionment. Coupling a geographic information system and a computation engine, we develop the Pangea framework, which offers a unique ability to discretize the globe using three-dimensional multi-scale grids, to overlay Eulerian fate and transport multimedia models, and to compute multi-pathway population exposure. We first apply this framework to predict the fate and transport of home and personal care chemicals in all of Asia. This study provides a large-scale high-resolution spatial inventory of emissions and a large data set of ~1,600 monitoring values. We compare predicted environmental concentrations (PECs) and measurements and find good agreement for the long-lived triclosan in fresh water (Pearson r=0.82), moderate agreement for shorter-lived substances, and a large discrepancy specifically for parabens in sediments. This study highlights the limitation of the present underlying gridded hydrological data set (WWDRII) when comparison with measurements at monitoring sites is required, which prompts the evaluation of a finer, catchment-based hydrological data set (HydroBASINS). We then focus on human exposure and the evolution of the population intake fraction with the distance from the source. We simulate emissions from 126 point sources (stacks of solid waste treatment plants) in France, and compute radial distributions of population intake fractions through inhalation and ingestion. We determine that a substantial fraction of emissions may be taken in by the population farther than 100 km away from point sources (78.5% of the inhaled benzene and 54.1% of the ingested 2,3,7,8-TCDD). We demonstrate the feasibility of simulating large numbers of emission scenarios by extending the study to 10,000 point sources. We finally extend the previous emitter-oriented studies with receptor-oriented analyses (source apportionment). We simulate 43 substances emitted from 4,101 point sources defined by the Australian National Pollutant Inventory for 2014-2015. We compute population exposure and severity (DALY). Formaldehyde, benzene, and styrene are the three top contributors in terms of DALYs. We demonstrate the technical feasibility of multimedia, large-scale source apportionment. This research opens new perspectives in spatial, local to large-scale fate and exposure modeling. The flexibility of Pangea allows to build project-specific model geometries and to re-analyze projects following the evolution of data availability. Major limitations come from the underlying first-order fate and transport models and from a limited availability of global spatial data sets.PHDEnvironmental Health SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/138610/1/wannaz_1.pd

Control Problems for Conservation Laws with Traffic Applications

Conservation and balance laws on networks have been the subject of much research interest given their wide range of applications to real-world processes, particularly traffic flow. This open access monograph is the first to investigate different types of control problems for conservation laws that arise in the modeling of vehicular traffic. Four types of control problems are discussed - boundary, decentralized, distributed, and Lagrangian control - corresponding to, respectively, entrance points and tolls, traffic signals at junctions, variable speed limits, and the use of autonomy and communication. Because conservation laws are strictly connected to Hamilton-Jacobi equations, control of the latter is also considered. An appendix reviewing the general theory of initial-boundary value problems for balance laws is included, as well as an appendix illustrating the main concepts in the theory of conservation laws on networks