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Assessing robustness and identifying vulnerabilities in deterministically coupled dynamical systems on complex networks

Applicant Jacquod Philippe
Number 182050
Funding scheme Project funding (Div. I-III)
Research institution HES-SO Valais
Institution of higher education University of Applied Sciences and Arts Western Switzerland - HES-SO
Main discipline Theoretical Physics
Start/End 01.11.2018 - 31.10.2022
Approved amount 835'528.00
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All Disciplines (3)

Discipline
Theoretical Physics
Mathematics
Electrical Engineering

Keywords (5)

Complex graphs and networks; Synchrony; Coupled dynamical systems; Nonlinear stability; Control under uncertainties

Lay Summary (French)

Lead
Évaluation de la robustesse et identification des vulnérabilités dans les systèmes dynamiques déterministes couplés sur des réseaux complexes
Lay summary
Les réseaux apparaissent naturellement dans pratiquement tous les domaines de la connaissance humaine - des sciences sociales aux sciences naturelles, en passant par les technologies de la communication, le génie électrique et les sciences de l'information. Ils donnent une représentation commode des systèmes complexes composés d’objets individuels discrets connectés les uns aux autres. L'état opérationnel des systèmes couplés sur réseau et leur dynamique sont déterminés par l'équilibre entre la dynamique intrinsèque de leurs composants et leur couplage. Dans la théorie des réseaux, deux questions d’importance centrale sont

(A) comment évaluer de manière fiable la robustesse globale d'un système,
(B) comment identifier rapidement et efficacement ses vulnérabilités locales.

Le problème (B) est lié au problème historique et fondamental de l'identification de "l'acteur clé" - par exemple, le joueur qui, une fois retiré, entraîne les changements les plus importants de l'activité des autres joueurs en théorie des jeux, ou le changement le plus important de structure d'un réseau social. Ce problème a été abordé avec l'introduction de descripteurs de réseaux, notamment les "indices de centralité". La moyenne des centralités sur l’ensemble du système fournit un indicateur global de la qualité de la liaison d’un réseau, ce qui facilite la résolution du problème (A). Des algorithmes très efficaces existent pour calculer ces indices - l'exemple le plus connu étant le PageRank de google - permettant un classement rapide des nœuds. Cette efficacité informatique rend les approches basées sur la centralité très attrayantes.

La recherche proposée consiste à développer des méthodes efficaces pour identifier les principaux acteurs des systèmes dynamiques couplés, dans le but d'évaluer efficacement leur robustesse globale et d'identifier leurs vulnérabilités locales. L'approche basée sur la centralité ne peut pas être appliquée directement à de tels systèmes, car les flux dans les systèmes dynamiques tels que les systèmes à oscillateur couplé, les réseaux électriques et les algorithmes de consensus dans les systèmes informatiques distribués sont déterministes.

L’objectif est de répondre aux questions :

Le système est-il globalement robuste contre les perturbations?

Le système est-il robuste face aux perturbations spécifiques ciblées?

Quelles perturbations spécifiques entraîneraient la pire réponse du système ?

Où ces perturbations spécifiques devraient-elles agir pour entraîner la pire réponse du système ?

Ces questions traitent ainsi des robustesses globale et spécifique des systèmes dynamiques couplés. La motivation est de construire des algorithmes de classement efficaces pour identifier rapidement et de manière fiable les vulnérabilités locales des systèmes couplés au réseau et sa robustesse globale face à un large spectre de perturbations, avec un impact potentiellement significatif sur la théorie du contrôle en particulier  de réseaux électriques.
Direct link to Lay Summary Last update: 03.10.2018

Responsible applicant and co-applicants

Employees

Associated projects

Number Title Start Funding scheme
154275 Systemic, Multi-Scale Approach to Integration of Renewable Energies in Electric Power Systems 01.08.2014 Assistant Professor (AP) Energy Grants

Abstract

Networks naturally occur in essentially all fields of human knowledge -- from social to natural sciences, communication technology, electrical engineering, information sciences and so forth. They conveniently represent complex systems composed of discrete individual objects connected to one another via binary relations. The operational state of network-coupled systems and their dynamics are determined by the balance between the intrinsic dynamics of their individual components and the coupling between them -- both the network-defined topology of the coupling and its dependence on system coordinates. In network theory, two issues of central importance are (A) how to reliably assess the global robustness of a network-coupled system, and (B) how to identify fast and efficiently its local vulnerabilities.Problem (B) is related to the historical and fundamental problem of identifying the "key player". That may be for instance the player who, once removed, leads to the biggest changes in the other player's activity in game theory, or to the biggest structural change in a social network. That problem has been tackled with the introduction of graph-theoretic descriptors, in particular "centrality indices". These indicators order nodes from the most "central" to the most "peripheral" -- they identify key players in a sense that they themselves define. Alternatively, centralities averaged over the whole system provide a global indicator of how tightly bound a network is, which helps in solving problem (A). A plethora of centrality indices have been introduced and discussed in the literature on network theory. As but one example, PageRank ranks nodes in decreasing order of the corresponding components of the Perron-Frobenius mode of a properly modified adjacency matrix defining a Markovian process on the graph. Very efficient algorithms exist to compute that mode, allowing for a fast ranking of the nodes even in very large networks. This computational efficiency makes centrality-based approaches very attractive. The proposed research is to develop efficient methods to identify key players in physical network-coupled dynamical systems, with the goal in mind to efficiently assess their global robustness and identify their local vulnerabilities. The centrality-based approach cannot be straightforwardly applied to such systems because flows in complex physical dynamical systems such as coupled oscillator systems, electric power grids and consensus algorithms in distributed computing systems are deterministic and not Markovian. They are determined by the coupling between individual components, in particular its functional dependence on system coordinates, and must satisfy physical conservation laws. Assessing such a network's global robustness and identifying its most critical components must therefore go beyond computing graph centralities and needs to incorporate the coupling dynamics into account. It is expectable that the most vulnerable components are not determined once and for all, but will change with the state of the system. It can furthermore be anticipated that local vulnerabilities against certain faults, perturbations or attacks will display resilience against other types of disturbances. Therefore the methodology I propose to follow takes into account the fact that "vulnerability" is not absolute, instead it depends on the operational state of the system, the nature of the disturbance and the performance measure used to assess the system's response. The approach will therefore (i) identify performance measures that are both physically sound and analytically tractable, (ii) consider a large spectrum of perturbations and disturbances (local and global; weak and strong; fluctuating, instantaneous or extended in time and so forth) and (iii) try and relate performance measures to local or global graph descriptors. The objective is to answer questions such as Is the network-coupled system in its current state globally robust against disturbances ?Is the network-coupled system in its current state robust against specific, targeted disturbances ?What specific disturbances would lead to the worst response of the network-coupled system ?Where should these specific disturbances act to lead to the worst response of the network-coupled system ?These questions deal with the global, average as well as the specific robustness of network-coupled dynamical systems. They will be addressed in small disturbance regimes and for stronger perturbations, with an emphasis put on trying to determine parametric boundaries between the two regimes. For strong perturbations, issues pertaining to cooperative phenomena, cascade of failures and long-range correlations of responses to perturbations will be investigated. The proposed research extends existing research directions and opens new ones in dynamical systems theory. The long-term motivation behind our research program is to construct efficient ranking algorithms to identify fast and reliably the local vulnerabilities in network-coupled systems and its overall robustness against a large spectrum of perturbations, with potentially significant impact on control theory and electrical power system engineering.
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