Dániel Leitold - Network-Based Analysis of Dynamical Systems: Methods for Controllability and Observability Analysis, and Optimal Sensor Placement

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Network science for the analysis of dynamical systems has become a widely applied methodology over the past decade. Representing the system as a mathematical graph enables several network-based methods to be applied and centrality and clustering measures calculated to characterise and describe the behaviour of dynamical systems. Through the application of network-related algorithms in complex interconnected systems, the methodology created a strong connection between computer science, control theory and other fields where the approach is applicable, e.g. in biology.

The key idea of this book is that the dynamical properties of complex systems can be determined by the effective calculation of specific structural features by network science-based analysis. Furthermore, certain dynamical behaviours can originate from the existence of specific motifs in the network representation or can be determined by network segmentation. Although the applicability of the methods and results was highlighted in the operability analysis of dynamical systems, the proposed methods can be utilised in various fields that will be mentioned at the end of each chapter.

Chapterof this book provides a brief introduction to the methodology that utilises the network science-based representation of dynamical systems to determine the location of the inputs and outputs such that their cardinality is also minimised. Then the scientific impact and main applications, e.g. in biology, sociology or physics, of the methodology are expounded on.

Chapterdeals with the structural analysis of the network-based representation of dynamical systems and defines those motifs that are specified by the dynamics of networks, e.g. integrating behaviour of a state variable, the diffusion of communication or changes in a temporal network. It was pointed out that these motifs are usually missing from benchmark networks. The significant reduction in the number of necessary inputs and outputs according to the presence of these motifs is also presented.

Chapterdeals with the improvement of the input and output configurations of dynamical systems, and presents five methods that can be used to decrease their relative degree according to the revealed motifs of the networks.

Chapterdeals with the analysis of the correlation between the structural properties of network-based representations and dynamical behaviours of dynamical systems. A general workflow is proposed, which was presented through a case study, that involved more than 600 heat exchanger networks.

Finally, an Octave- and MATLAB-compatible toolbox is introduced which is capable of conducting the analysis introduced in the previous chapters. The implemented functions are presented in the form of an artificial example that clearly shows the connection between the structural as well as dynamical features and highlights the differences between the centrality measures.