Partial Moments in System Identification

This book provides a complete round-up of developments concerned with the application of partial moments in system identification and data-driven modelling; it captures the essence of work carried out at the Laboratoire d’Informatique et d’Automatique pour les Systèmes for more than 40 years.

The book begins with introductory material, describing both the mathematical tools associated with partial moments and reinitialized partial moments and an example demonstrating their use. The authors then proceed to show how these tools can be used for the identification of continuous-time linear models, discrete-time linear models, continuous-time linear state-space models, linear parameter-varying models and multidimensional models based on partial differential equations. The properties and performances of each of these approaches are presented. The analogy with algebraic approaches is proved, thus opening perspectives for extension to other fields. The text removes some long-standing limitations on the implementation of partial-moment-based tools in system identification.

This book is of interest to researchers and postgraduates studying system identification, control theory, applied mathematics and computer science. It is also useful for engineers working on industrial applications of the parametric estimation of mathematical models.

Régis Ouvrard did all his graduate studies at the University of Poitiers: M.S. degree in Electronics, Electrical Engineering and Automation in 1992, Certificate of aptitude for secondary school teachers in Electronics in 1996, Ph.D. degree in Automatic Control in 1997 and Accreditation to supervise research in 2022. Since 1999, he has been an associate professor at the University Institute of Technology in Poitiers.

His research topics are dedicated to system identification and data-driven modelling. He has contributed significantly to the dissemination of the tools based on partial moments in system identification.

The common denominator in the application of the tools that Régis Ouvrard develops is the protection of the environment and biodiversity. For example, he is currently proposing new population dynamics models to study the impacts of global changes on biodiversity.

Thierry Poinot received his Ph.D. in 1996 from the University of Poitiers, France, in the field of automatic control. He has been a professor at the University of Poitiers since 1996. He is a member of the Computer Science and Automatic Control for Systems Laboratory at the University of Poitiers, of which he has been the director since 2022. His research interests are in the areas of system identification and data-driven modelling, including the identification of linear and nonlinear continuous-time systems, the identification of linear parameter-varying systems, and the modelling and identification of fractional systems. His current activities focus on modelling and identifying Li-ion batteries and modelling population dynamics applied to biodiversity.

Jean-Claude Trigeassou received the Maîtrise EEA diploma from the University of Bordeaux in 1969, the French Agrégation of applied physics in 1971, the Ph.D. degree and the Doctorat d’Etat in automatic control in 1981 and 1987. From 1988 to 2006, he has been a professor at ESIP in Poitiers University. Since his retirement, he developed an original theory entitled Infinite State Representation of fractional order differential systems.

His first thesis was dedicated to the method of moments with applications to identification and control. Then, he defined and developed the reinitialized partial moment theory and its application to the identification of discrete and continuous-time systems. In parallel, he has investigated output error identification methodology and particularly parameter estimation of continuous systems with application to the diagnosis of electrical machines.