Modeling of physical network systems

Conservation laws and balance equations for physical network systems typically can be described with the aid of the incidence matrix of a directed graph, and an associated symmetric Laplacian matrix. Some basic examples are discussed, and the extension to k-complexes is indicated. Physical distribution networks often involve a non-symmetric Laplacian matrix. It is shown how, in case the connected components of the graph are strongly connected, such systems can be converted into a form with balanced Laplacian matrix by constructive use of Kirchhoffs Matrix Tree theorem, giving rise to a port-Hamiltonian description. Application to the dual case of asymmetric consensus algorithms is given. Finally it is shown how the minimal storage function for physical network systems with controlled flows can be explicitly computed. (C) 2015 Elsevier B.V. All rights reserved

Evolution of social power over influence networks containing antagonistic interactions

Individual social power in the opinion formation process over social influence networks has been under intense scientific investigation. Most related works assume explicitly or implicitly that the interpersonal influence weights are always non-negative. In sharp comparison, we argue that such influence weights can be both positive and negative since there exist various contrasting relationships in real-world social networks. Hence, this article studies the evolution of opinion dynamics and social power on cooperative-competitive networks whose influence structure changes via a reflected appraisal mechanism along a sequence of issue discussions. Of particular focus is on identifying the pathways and effects of social power on shaping public opinions from a graph-theoretic perspective. Then, we propose a dynamic model for the reflected self-appraisal process, which enables us to discuss how the individual social power evolves over sequential issue discussions. By accommodating differential Lyapunov theory, we show the global exponential convergence of the self-appraisal model for almost all network topologies. Finally, we conclude that the self-appraisals and social powers are eventually dependent only on an interpersonal appraisal profile

Model Reduction Methods for Complex Network Systems

Network systems consist of subsystems and their interconnections, and provide a powerful framework for analysis, modeling and control of complex systems. However, subsystems may have high-dimensional dynamics, and the amount and nature of interconnections may also be of high complexity. Therefore, it is relevant to study reduction methods for network systems. An overview on reduction methods for both the topological (interconnection) structure of the network and the dynamics of the nodes, while preserving structural properties of the network, and taking a control systems perspective, is provided. First topological complexity reduction methods based on graph clustering and aggregation are reviewed, producing a reduced-order network model. Second, reduction of the nodal dynamics is considered by using extensions of classical methods, while preserving the stability and synchronization properties. Finally, a structure-preserving generalized balancing method for simplifying simultaneously the topological structure and the order of the nodal dynamics is treated.Comment: To be published in Annual Review of Control, Robotics, and Autonomous System

A graph-based modelling methodology for high-pressure networks applied on waterjet machining

This paper proposes a graph-based methodology that models high-pressure networks of varioustopologies. Therefore, a mathematical modelling of a supply network for waterjet machining will be introduced. High-pressure components are assigned to homogeneous segments, each representing a local pressure state as a differential equation. Segments are subsequently interconnected along the fluid flow path as an algebraic equation that allocates a fluid flow to the interconnections, resulting in a lumped parameter model. For this purpose, a graph network description has been used to approximate the spatially distributed high-pressure system. In this way, the proposed methodology offers a flexible modelling to cope with different network topologies. Moreover, a variable fluid compressibility has also been introduced so that a wide operating range can be included. This modelling methodology has been applied to a supply network for waterjet machining. The resulting mathematical model has been verified by measurements from a test bench with a pressure range of 100 to 400 MPa. It was shown that a variable fluid compressibility improves the model’s accuracy and that modelling errors can be reduced in comparison to other existing methodologies