Over the past two decades large-scale networks of interconnected dynamic systems have captured great attention among researchers and practitioners concerned with control system design. This activity results from rapid technological advances in hardware and software related to communication networks, enabling an outburst of emerging challenging applications. Dynamic subsystems forming a network of this type communicate with one another, thereby mutually influencing their input-output behaviours. The interconnections in this context can exist physically or be purely logical (when local subsystems simply exchange data). Representative examples are networks of pipelines and electrical grids, offshore wind farms, or smart materials for active wing control in aeroplanes. They also include partial differential equations modelling spatio-temporal processes. Indeed, once discretized in space, they can be interpreted as arrays of local dynamic systems.
The monograph written by Verhaegen, Yu and Sinquin is focused specifically on identification of networks of linear dynamic systems. Its contents furnish incontestable proofs that this vital and extremely challenging research area is no longer in its infancy and is already supported by non-trivial theory and quite advanced identification techniques. An invaluable asset of this monograph is that it is written by solid researchers who have specialized in system identification for many years. The book has grown out of both their pioneering work and the painstaking efforts made by more and more researchers interested in this field. Thus, it offers an excellent and informative overview of the state of the art by giving a full account of information scattered in numerous papers, reports and unpublished works. Beyond any doubt, an invaluable addition is a detailed investigation reported on employing the new identification methods for the real-life case study of adaptive optics. Such formidable and intriguing applications rarely complement monographs dealing with sophisticated aspects of systems analysis.
The monograph consists of three major parts. The first of them (Chapters 2 to 5) constitutes an overview of the mathematical models of large-scale network-connected systems with particular emphasis on their parametrization. This is a key aspect since a great difficulty in directly adapting traditional identification methods to large-scale networks are tremendous volumes of data and the large number of parameters necessary to describe these models. Therefore, various model structures, originating in both input-output transfer function models and state-space models, are discussed, with a trade-off between the number of parameters and model accuracy. The second part (Chapters 6 to 9) is the main piece of the monograph, centred around novel identification techniques for large-scale network connections of linear dynamic systems. First, transfer-function-type models are worked on in combination with signal graph models. Owing to the globality of the approach (full models are to be identified using all available data), the sparsity in the model parametrization becomes of paramount importance. To get this property, heavy use is made of the particular geometry or sensor grid features to derive structure in the coefficient matrices of the models. Second, network connections of linear state-space models with dedicated structures of system matrices are investigated. For them, subspace-like identification methods are developed so as to exploit data to deduce the sizes of blocks of these matrices and estimate the parameters in these blocks. As a result, identification of local systems in a large network using only local data is made possible. Finally, apart from traditional settings of maximum-likelihood or expectation-maximization methods, a new method is outlined, which approaches the underlying non-convex parameter optimization problem via difference of convex functions optimization. The third part (Chapter 10) demonstrates applications of most presented methods to a case study regarding adaptive optics. The trade-off between the scalability of the proposed algorithms and the model performance is brought into focus. The three parts are complemented with an overview of prospective research challenges and the appropriate software development, accessory appendices on properties of the Kronecker product and tensors, and a very long list of references pertaining to the material outlined in the book.
Overall, the monograph is a solid piece of work on a subject that attracts considerable attention. The authors supply a unique presentation that incorporates ideas from the areas of system identification, network-connected systems and numerical algorithms. They have managed to set forth a systematic approach to key identification techniques including the most recent advances in systems analysis and control of network-connected systems. Extremely interesting applications highlight the relevance of the presented concepts. This can be an excellent book for a graduate-level course in identification of network-connected systems, as well as an extremely valuable reference for beginning Ph.D. students, researchers and engineers interested in modern system identification of complex dynamic systems.