Measurements, Models, Systems and Design

531 s.

Structure-Preserving Model Reduction of Physical Network Systems

This paper considers physical network systems where the energy storage is naturally associated to the nodes of the graph, while the edges of the graph correspond to static couplings. The first sections deal with the linear case, covering examples such as mass-damper and hydraulic systems, which have a structure that is similar to symmetric consensus dynamics. The last section is concerned with a specific class of nonlinear physical network systems; namely detailed-balanced chemical reaction networks governed by mass action kinetics. In both cases, linear and nonlinear, the structure of the dynamics is similar, and is based on a weighted Laplacian matrix, together with an energy function capturing the energy storage at the nodes. We discuss two methods for structure-preserving model reduction. The first one is clustering; aggregating the nodes of the underlying graph to obtain a reduced graph. The second approach is based on neglecting the energy storage at some of the nodes, and subsequently eliminating those nodes (called Kron reduction).</p

Sliding Mode Control

The main objective of this monograph is to present a broad range of well worked out, recent application studies as well as theoretical contributions in the field of sliding mode control system analysis and design. The contributions presented here include new theoretical developments as well as successful applications of variable structure controllers primarily in the field of power electronics, electric drives and motion steering systems. They enrich the current state of the art, and motivate and encourage new ideas and solutions in the sliding mode control area

Analyse et commande des systèmes paramétrés, par la fonction signe matricielle

This thesis focuses on some new methods for analysis and control problems of parameter-dependent systems. These problems are reformulated as a parameter-dependent Riccati, Lyapunov and/or Sylvester equation.As an alternative to the LMI framework, we show initially that these problems can be solved thanks to the matrix sign function, or direct inversion methods of parameter-dependent matrices.Several approaches are proposed along the manuscript. First the use of non-iterative methods, based either on a direct inversion method, or on the integral definition of the matrix sign function is proposed.A second way mixes the matrix sign function together with the spectral decomposition of a matrix in an original method for the solution of non-standard Sylvester equations.Then, several methods, called iterative methods, are also proposed based on different mathematic tools such as the Laurent polynomial expansion, the inverse via Discrete Fourier Transform, etc.All along the manuscript, examples are shown, simultaneously in the constant and parameter-dependent cases, in order to show to the reader the applicability and the limits of the proposed methods.La thèse présentée ici a pour objet de proposer des méthodes de résolution de problèmes d’analyse et de commande de systèmes paramétrés. Ces problèmes sont ramenés à la résolution d’équations de Riccati, de Lyapunov et/ou de Sylvester paramétrées.S’inscrivant comme une alternative au formalisme LMI nous montrons dans un premier temps que ces équations peuvent être résolues à l’aide de la fonction signe matricielle ou des méthodes d’inversion directe de matrices paramétrées.Différentes approches sont proposées tout au long du manuscrit. On notera dans un premier temps l’utilisation de méthodes non itératives, se basant soit sur une méthode d’inversion directe, soit sur la définition dite intégrale de la fonction signe matricielle. Une seconde voie explorée combine la fonction signe matricielle avec la séparation de spectre d’une matrice pour la résolution d’équations de Sylvester non standards. Ensuite, différentes méthodes, dites itératives, sont proposées également se basant sur des outils mathématiques tels que l’expansion en polynômes de Laurent, les inversions de Fourier, etc. Tout au long du manuscrit, des exemples sont proposés, tant sur le plan constant que paramétré afin d’estimer l’applicabilité, l’efficacité ainsi que les limites des différentes méthodes proposées

Discrete Event Simulations

Considered by many authors as a technique for modelling stochastic, dynamic and discretely evolving systems, this technique has gained widespread acceptance among the practitioners who want to represent and improve complex systems. Since DES is a technique applied in incredibly different areas, this book reflects many different points of view about DES, thus, all authors describe how it is understood and applied within their context of work, providing an extensive understanding of what DES is. It can be said that the name of the book itself reflects the plurality that these points of view represent. The book embraces a number of topics covering theory, methods and applications to a wide range of sectors and problem areas that have been categorised into five groups. As well as the previously explained variety of points of view concerning DES, there is one additional thing to remark about this book: its richness when talking about actual data or actual data based analysis. When most academic areas are lacking application cases, roughly the half part of the chapters included in this book deal with actual problems or at least are based on actual data. Thus, the editor firmly believes that this book will be interesting for both beginners and practitioners in the area of DES