Showing papers by "Wpmh Maurice Heemels published in 2001"
TL;DR: Equivalences among five classes of hybrid systems are established, of paramount importance for transferring theoretical properties and tools from one class to another, with the consequence that for the study of a particular hybrid system that belongs to any of these classes, one can choose the most convenient hybrid modeling framework.
780 citations
04 Dec 2001
TL;DR: In this paper, a simple and direct proof that the closed-loop system (cl-MPC) is a subclass of any of the former five classes of hybrid systems was provided.
Abstract: The following five classes of hybrid systems were proved by W.P.M.H. Heemels et al. (2001) to be equivalent: linear complementarity (LC) systems, extended linear complementarity (ELC) systems, mixed logical-dynamical (MLD) systems, piecewise affine (PWA) systems and max-min-plus-scaling (MMPS) systems. Some of the equivalences were obtained under additional assumptions, such as boundedness of system variables. In this paper, for closed-loop linear or hybrid plants with model-predictive control (MPC) based on a linear model and fulfilling linear constraints on the input and state variables, we provide a simple and direct proof that the closed-loop system (cl-MPC) is a subclass of any of the former five classes of hybrid systems. This result opens up the use of tools developed for hybrid systems (such as stability, robust stability and safety analysis tools) to study the closed-loop properties of MPC.
42 citations
04 Dec 2001
TL;DR: In this article, the equivalences among five classes of hybrid systems, namely mixed logical dynamical systems, linear complementarity systems, extended linear complements, piecewise affine systems, and max-min-plus-scaling systems, were established.
Abstract: We establish equivalences among five classes of hybrid systems, that we have encountered in previous research: mixed logical dynamical systems, linear complementarity systems, extended linear complementarity systems, piecewise affine systems, and max-min-plus-scaling systems. These results are of paramount importance for transferring properties and tools from one class to another.
39 citations
TL;DR: In this article, the authors study the well-posedness of linear relay systems with respect to two different solution concepts, and derive necessary and sufficient conditions for wellposedness in the sense of Filippov of linear systems of relative degree one and two in closed loop with relay feedback.
10 citations
01 Jan 2001
TL;DR: In this article, the authors study linear passive electrical circuits mixed with ideal diodes and voltage/current sources within the framework of linear complementarity systems and investigate the existence and uniqueness of solution trajectories.
Abstract: In this paper we study linear passive electrical circuits mixed with ideal diodes and voltage/current sources within the framework of linear complementarity systems. Linear com- plementarity systems form a subclass of hybrid dynamical systems and as such questions about existence and uniqueness of solution trajectories are non-trivial and will be investigated here. The nature of the behaviour is analyzed and characterizations of the inconsistent states and explicit jump rules are presented in various equivalent forms. Moreover, the mode-selection problem (determining the discrete state as a function of the continuous state) will be discussed as well. The characterizations and rules will be in terms of quadratic programming problems and linear complementarity problems for which many numerical algorithms are available. As a consequence, the results obtained in this paper lead to numerical approaches for problems appearing in the event-driven simulation of a class of switched electrical circuits. A detailed example will illustrate the obtained results. RESUME. Dans le cadre des systemes lineaires complementaires, cet article porte sur l'etude de circuits electriques lineaires passifs, comportant des diodes ideales et des sources de ten- sion/courant. Les systemes lineaires complementaires constituent une sous-classe de systemes dynamiques hybrides, entrainant ainsi des problemes non triviaux d'existence et d'unicite des trajectoires qui seront plus particulierement abordes. Plusieurs formes d'equivalence sont uti- lisees pour analyser le comportement et identifier les etats incoherents ainsi que les regles de sauts explicites. Le probleme de la selection du mode discret en fonction de l'etat continu sera egalement traite. Les resultats obtenus fournissent des solutions numeriques aux problemes relatifs a la simulation evenementielle d'une classe de circuits electriques a commutation. Un exemple est donne pour illustrer ces resultats.
9 citations
01 Jan 2001
TL;DR: Concerns mailing systems that automatically assemble mailings consisting of several brochures that involves synchronization between one master (the conveyor belt) and many slaves.
Abstract: Concerns mailing systems that automatically assemble mailings consisting of several brochures. The main component of the mailing (e.g. a book or a magazine) enters the conveyor belt (lug chain) at the loader module. Several supplements are added to the main product by a feeder module consisting of sheet-feeders. Sheet-feeders basically grab a brochure from a stack and put it on the conveyor belt (the master in this case). The main product, together with the supplements, form a package that is wrapped in plastic foil by a packaging module. The foil is supplied by a reel stand. Incorrect packages are removed at the rejection module. Finally, the product is released after which an address is printed on it, using a label or directly, via an inkjet printer. After this the product is put on a stack. The paper describes the control of the system, which involves synchronization between one master (the conveyor belt) and many slaves.
1 citations