PhD position: EVOLUTIONARY SCALE-FREE MODELS FOR LARGE SCALE COMPLEX NETWORKS
NeCS group (joint CNRS (GIPSA-lab)-INRIA team), in Collaboration with the University of Padova.
Supervisors: Carlos Canudas-de-Wit (CNRSmain supervisor), Sandro Zampieri (UDP co-supervisor).
Context: ERC-AdG Scale-FreeBack
TOPIC DESCRIPTION. This research proposal deals with the problem of setting up a suitable modelling framework for complex systems corresponding to large-scale networks. The original system is assumed to describe a homogenous network in which the node/link distribution of G gives a bell-shaped, exponentially decaying curve. Homogenous networks cover many critical systems of interest (such as road traffic networks, power grids, water distribution systems, etc.), but are inherently complex. Scale-FreeBack is elaborated on the idea that complexity can be broken down by abstracting an aggregated scale-free model (represented by a network with a power law degree distribution), by merging/lumping neighboring nodes in the original network. In that, supper-nodes (nodes with a lot of connections) are created and represented by “aggregated” variables. Controlling only boundary inputs and observing only aggregated variables allows to cut-off the system complexity.
The following questions will be addressed:
- Defining the most suitable level of aggregation for the model. This boils down to defining and sizing the state-vector, the control inputs and outputs. A first question is how to define the right level of aggregation, and investigate new metrics trading quantifiers reflecting an optimal level of scalability (a suited node/link distribution) of the associated network graph, with other performance indexes reflecting the system’s closed-loop operation.
- The second question focuses on how the aggregation process, in addition to the scale-free property, will yield models consistent with the design of control and the observation goals. The aggregation process will have to include observability and controllability properties which are consistent with the evolutionary nature of scale-free aggregated models (aggregation process is evolutionary in the sense that the network changes and so the aggregated modules will change accordingly while preserving the scale-free properties).
- Finally, innovative concepts such as peripheral controllability (i.e. controlling the boundary flows in a lumped node rather than controlling each single node separately), and energy-weighted controllability metrics (where controllability is qualified by assessing the energy costs as a function of the controllable nodes [Zam-et-al’14]) will be extended in this project to the context of scale-free models. While only open loop metrics have been considered so far, we aim to propose new closed loop metrics also taking inspiration from road traffic networks application. Moreover we intend to extend these concepts to the estimation and monitoring by investigating the observability of aggregated networks. Finally, we will propose and investigate different new weak notions of controllability/observability in which the controllability/observability is determined with respect to a limited subspace (peripheral and/or sparse controllability/observability)
QUALIFICATIONS: knowledge and mathematical background in systems and control theory, Complex and/or networked controlled systems.
EMPLOYMENT AND CONTEXT: This full-time position for 3 years. The position will be open from Sept 2016 until filled. In our NeCS team at Grenoble, we offer a dynamical research environment with a strong activity in networked controlled systems. This PhD position is part of the large research project Scale-FreeBack ERC Advanced Grant 2016-2021. The ERC is hosted by the CNRS, and the project will be conducted within the NeCS group (which is a joint CNRS (GIPSA-lab)-INRIA team).
APPLICATIONS: Please follow instructions here: http://www.gipsa-lab.grenoble-inp.fr/~carlos.canudas-de-wit/ERC.php