On the modelling and analysis of complex dynamic networks

Abstract

The efficient, reliable, and fault tolerant operation of complex dynamical networks underpins a diverse number of technologies and capabilities. Many of these capabilities are fundamental to society's operation and include the electricity network that delivers power, the Internet that delivers information, and complex dynamic systems like modern aircraft and buildings that deliver important services. This thesis addresses a number of open problems in the modelling and analysis of complex dynamical networks, utilising ideas and methodologies drawn from the systems and control, computer science and artificial intelligence, and diagnosis and fault tolerance domains. Important modelling paradigms for complex dynamic networks are presented that provide insight into a number of important problems. The models emerge from a simple insight; namely that a complex dynamic network consists of dynamical systems that are connected through their inputs and outputs. Specifically, the interconnections are formed through the output of one system being an input to other systems in the network. This viewpoint leads to the development of linear, linear structured, nonlinear, and hybrid network models that underpin the results obtained in this thesis. These network models allow an investigation into the controllability of complex dynamic systems to be undertaken. Most importantly these results show how the global controllability of inter-connected dynamical systems relies only on the local controllability properties of each system in the network as well as the interconnection topology of those systems. This is a fundamentally important result because it highlights that global properties of the network can be determined using local properties of the individual systems in the network. Algorithms for recursive sparse regression and their application to determine the interconnection structure of dynamical networks are also presented in this thesis. These algorithms offer the capability to recursively determine sparse parameter estimates as well as to determine Bayesian credible statistics about the parameter estimates obtained. This thesis also addresses a number of problems in the detection and isolation of faults in complex hybrid dynamical networks. These results include those on the structural diagnosability of complex dynamical networks, the use of estimation techniques for change point detection in hybrid systems and methods of detecting and isolating faults in large complex dynamical networks. The latter results are very general and apply to any form of event driven systems. Throughout the thesis a number of pertinent examples are presented and important future work is addressed. This thesis is an important step towards integrating a number of important viewpoints on complex dynamic networks and outlines many opportunities for future work that will result in a better understanding of the operation of complex dynamical networks. Show more