Large scale heterogeneous networks, the Davis-Wielandt shell, and graph separation

We consider a large scale network of interconnected heterogeneous dynamical components. Scalable stability conditions are derived that involve the input/output properties of individual subsystems and the interconnection matrix. The analysis is based on the Davis-Wielandt shell, a higher dimensional version of the numerical range with important convexity properties. This can be used to allow heterogeneity in the agent dynamics while relaxing normality and symmetry assumptions on the interconnection matrix. The results include small gain and passivity approaches as special cases, with the three dimensional shell shown to be inherently connected with corresponding graph separation arguments. © 2012 Society for Industrial and Applied Mathematics.

Project neptune: Improved operation of water distribution networks

Water service providers (WSPs) in the UK have statutory obligations to supply drinking water to all customers that complies with increasingly stringent water quality regulations and minimum flow and pressure criteria. At the same time, the industry is required by regulators and investors to demonstrate increasing operational efficiency and to meet a wide range of performance criteria that are expected to improve year-on-year. Most WSPs have an ideal for improving the operation of their water supply systems based on increased knowledge and understanding of their assets and a shift to proactive management followed by steadily increasing degrees of system monitoring, automation and optimisation. The fundamental mission is, however, to ensure security of supply, with no interruptions and water quality of the highest standard at the tap. Unfortunately, advanced technologies required to fully understand, manage and automate water supply system operation either do not yet exist, are only partially evolved, or have not yet been reliably proven for live water distribution systems. It is this deficiency that the project NEPTUNE seeks to address by carrying out research into 3 main areas; these are: data and knowledge management; pressure management (including energy management); and the associated complex decision support systems on which to base interventions. The 3-year project started in April of 2007 and has already resulted in a number of research findings under the three main research priority areas (RPA). The paper summarises in greater detail the overall project objectives, the RPA activities and the areas of research innovation that are being undertaken in this major, UK collaborative study. Copyright 2009 ASCE.

Scalable robustness for consensus protocols with heterogeneous dynamics

It is shown in the paper how robustness can be guaranteed for consensus protocols with heterogeneous dynamics in a scalable and decentralized way i.e. by each agent satisfying a test that does not require knowledge of the entire network. Random graph examples illustrate that the proposed certificates are not conservative for classes of large scale networks, despite the heterogeneity of the dynamics, which is a distinctive feature of this work. The conditions hold for symmetric protocols and more conservative stability conditions are given for general nonsymmetric interconnections. Nonlinear extensions in an IQC framework are finally discussed. Copyright © 2005 IFAC.