2,706 research outputs found
Switched networks and complementarity
A modeling framework is proposed for circuits that are subject both to externally induced switches (time events) and to state events. The framework applies to switched networks with linear and piecewise-linear elements, including diodes. We show that the linear complementarity formulation, which already has proved effective for piecewise-linear networks, can be extended in a natural way to also cover switching circuits. To achieve this, we use a generalization of the linear complementarity problem known as the cone-complementarity problem. We show that the proposed framework is sound in the sense that existence and uniqueness of solutions is guaranteed under a passivity assumption. We prove that only first-order impulses occur and characterize all situations that give rise to a state jump; moreover, we provide rules that determine the jump. Finally, we show that within our framework, energy cannot increase as a result of a jump, and we derive a stability result from this
Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems
The present article presents a summarizing view at differential-algebraic
equations (DAEs) and analyzes how new application fields and corresponding
mathematical models lead to innovations both in theory and in numerical
analysis for this problem class. Recent numerical methods for nonsmooth
dynamical systems subject to unilateral contact and friction illustrate the
topicality of this development.Comment: Preprint of Book Chapte
Handling congestion in crowd motion modeling
We address here the issue of congestion in the modeling of crowd motion, in
the non-smooth framework: contacts between people are not anticipated and
avoided, they actually occur, and they are explicitly taken into account in the
model. We limit our approach to very basic principles in terms of behavior, to
focus on the particular problems raised by the non-smooth character of the
models. We consider that individuals tend to move according to a desired, or
spontanous, velocity. We account for congestion by assuming that the evolution
realizes at each time an instantaneous balance between individual tendencies
and global constraints (overlapping is forbidden): the actual velocity is
defined as the closest to the desired velocity among all admissible ones, in a
least square sense. We develop those principles in the microscopic and
macroscopic settings, and we present how the framework of Wasserstein distance
between measures allows to recover the sweeping process nature of the problem
on the macroscopic level, which makes it possible to obtain existence results
in spite of the non-smooth character of the evolution process. Micro and macro
approaches are compared, and we investigate the similarities together with deep
differences of those two levels of description
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