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NIAZI Muhammad Umar B

Aggregated Monitoring of Large-scale Network Systems and Control of Epidemics

 

Directeur de thèse :     Carlos CANUDAS-DE-WIT

Co-directeur de thèse :     Alain KIBANGOU

École doctorale : Electronique, electrotechnique, automatique, traitement du signal (EEATS)

Spécialité : Automatique et productique

Structure de rattachement : INRIA

Établissement d'origine : Bilkent University - Turquie

Financement(s) : Erc ; contrat à durée déterminée ; Sans financement

 

Date d'entrée en thèse : 01/12/2017

Date de soutenance : 12/07/2021

 

Composition du jury :

GEORGES Didier, Professeur des universités, Grenoble-INP, Président EFIMOV Denis, Directeur de recherche, Inria Lille, Rapporteur
IMURA Jun-ichi, Professeur des universités, Tokyo Institute of Technology, Rapporteur
SCHERPEN Jacquelien, Professeur des universités, University of Groningen, Examinatrice
JOHANSSON Karl Henrik, Professeur des universités, KTH Royal Institute of Technology, Examinateur
BLIMAN Pierre-Alexandre, Directeur de recherche, Inria Paris, Invité

 

Résumé :
This Ph.D. thesis is done mainly in the context of the European Research Council's (ERC) Advanced Grant project Scale-FreeBack and partially in the context of the Inria's COVID-19 Mission project Healthy-Mobility. The Scale-FreeBack project aims to develop a holistic, scale-free control approach to complex systems and to set new foundations for a theory dealing with complex physical networks with arbitrary dimensions. On the other hand, motivated by the onset of the COVID-19 pandemic, the Healthy-Mobility project aims to develop optimal control strategies for testing and urban human mobility to limit the epidemic spread. In relation to both projects, the contributions of the thesis are respectively divided into two parts.
In the first part of the thesis, we develop a theory for monitoring large-scale clustered network systems with limited computational and sensing equipment through a projected network system, which is of tractable dimension and is obtained through the aggregation of clusters of a network system. We propose a minimum-order average observer and provide its design criteria. Then, the notions of average reconstructability, average observability, and average detectability are defined and their necessary and sufficient conditions are provided. We also provide graph-theoretic interpretations of these notions through inter-cluster and intra-cluster graph topologies of a clustered network system. When a clustered network system does not meet the design criteria of the average observer, we devise an optimal design methodology to minimize the average estimation error. On the other hand, if the clusters are not pre-specified in a network system, we develop clustering algorithms to achieve minimum average estimation error. Finally, we propose a K-means type clustering approach to estimate the state variance of network systems, which is a nonlinear functional of the state vector and measures the squared deviation of state trajectories from their average mean. We illustrate the results through application examples of a building thermal system and an SIS epidemic spread over large networks.
In the second part of the thesis, we first study epidemic suppression through a testing policy. We develop a five-compartment epidemic model that incorporates the testing rate as a control input. We propose a best-effort strategy for testing (BEST), which is an epidemic suppression policy that provides a minimum testing rate from a certain day onward to stop the growth of the epidemic. The BEST policy is evaluated through its impact on the number of active intensive care unit (ICU) cases and the cumulative number of deaths for the COVID-19 case of France. Secondly, we develop a model of urban human mobility between residential areas and social destinations such as industrial areas, business parks, schools, markets, etc. for epidemic mitigation. We formulate two optimal control policies, the so-called optimal capacity control (OCC) and optimal schedule control (OSC), that aims to maximize the economic activity in an urban environment while keeping the number of active infected cases bounded. The OCC limits the epidemic spread by reducing the maximum number of people allowed at each destination category at any time of day, whereas the OSC limits the epidemic spread by reducing the daily business hours of each destination category.


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