Interior feedback stabilization of wave equations with dynamic boundary delay

In this paper we consider an interior stabilization problem for the wave equation with dynamic boundary delay.We prove some stability results under the choice of damping operator. The proof of the main result is based on a frequency domain method and combines a contradiction argument with the multiplier technique to carry out a special analysis for the resolvent

Delays, Inaccuracies and Anticipation in Microscopic Traffic Models

We generalize a wide class of time-continuous microscopic traffic models to include essential aspects of driver behaviour not captured by these models. Specifically, we consider (i) finite reaction times, (ii) estimation errors, (iii) looking several vehicles ahead (spatial anticipation), and (iv) temporal anticipation. The estimation errors are modelled as stochastic Wiener processes and lead to time-correlated fluctuations of the acceleration. We show that the destabilizing effects of reaction times and estimation errors can essentially be compensated for by spatial and temporal anticipation, that is, the combination of stabilizing and destabilizing effects results in the same qualitative macroscopic dynamics as that of the respectively underlying simple car-following model. In many cases, this justifies the use of simplified, physics-oriented models with a few parameters only. Although the qualitative dynamics is unchanged, multi-anticipation increase both spatial and temporal scales of stop-and-go waves and other complex patterns of congested traffic in agreement with real traffic data. Remarkably, the anticipation allows accident-free smooth driving in complex traffic situations even if reaction times exceed typical time headways.Comment: Major revision of the model and the simulations. Particularly, the number of model parameters has been reduce

A New Formulation of the Initial Value Problem for Nonlocal Theories

There are a number of reasons to entertain the possibility that locality is violated on microscopic scales, for example through the presence of an infinite series of higher derivatives in the fundamental equations of motion. This type of nonlocality leads to improved UV behaviour, novel cosmological dynamics and is a generic prediction of string theory. On the other hand, fundamentally nonlocal models are fraught with complications, including instabilities and complications in setting up the initial value problem. We study the structure of the initial value problem in an interesting class of nonlocal models. We advocate a novel new formulation wherein the Cauchy surface is "smeared out" over the underlying scale of nonlocality, so that the the usual notion of initial data at t=0 is replaced with an "initial function" defined over -M^{-1} \leq t \leq 0 where M is the underlying scale of nonlocality. Focusing on some specific examples from string theory and cosmology, we show that this mathematical re-formulation has surprising implications for the well-known stability problem. For D-brane decay in a linear dilaton background, we are able to show that the unstable directions in phase space cannot be accessed starting from a physically sensible initial function. Previous examples of unstable solutions in this model therefore correspond to unphysical initial conditions, an observation which is obfuscated in the old formulation of the initial value problem. We also discuss implication of this approach for nonlocal cosmological models.Comment: 36 pages, 9 figures. Accepted for publication in Nuclear Physics

Suppression of axial-torsional vibrations in drilling system described by neutral-type delay differential equations

Vibrations in deep drilling systems lead to efficiency deterioration and may even cause the system failure. In this paper, a controller is designed aiming at mitigation of these vibrations, which is based on a neutral-type time delay model that represents distributed axial and torsional dynamics. First, the stability of the associated linearized dynamics is analyzed using a spectral approach. Furthermore, the open-loop system is shown to be stabilizable by state feedback which supports subsequent controller design. An optimization-based continuous pole placement technique has been employed to design a stabilizing controller, which mitigates steady-state drill-string vibrations. The effectiveness of the controller is shown in a representative case study

Single-file pedestrian dynamics: a review of agent-following models

Single-file dynamics has been studied intensively, both experimentally and theoretically. It shows interesting collective effects, such as stop-and-go waves, which are validation cornerstones for any agent-based modeling approach of traffic systems. Many models have been proposed, e.g. in the form of car-following models for vehicular traffic. These approaches can be adapted for pedestrian streams. In this study, we delve deeper into these models, with particular attention on their interconnections. We do this by scrutinizing the influence of different parameters, including relaxation times, anticipation time, and reaction time. Specifically, we analyze the inherent fundamental problems with force-based models, a classical approach in pedestrian dynamics. Furthermore, we categorize car-following models into stimulus-response and optimal velocity models, highlighting their historical and conceptual differences. These classes can further be subdivided considering the conceptual definitions of the models, e.g. first-order vs. second-order models, or stochastic vs. deterministic models with and without noise. Our analysis shows how car-following models originally developed for vehicular traffic can provide new insights into pedestrian behavior. The focus on single-file motion, which is similar to single-lane vehicular traffic, allows for a detailed examination of the relevant interactions between pedestrians.Comment: 35 pages, 10 Figures; chapter accepted for publication in Crowd Dynamics (vol. 4

Suppression of axial-torsional vibrations in drilling system described by neutral-type delay differential equations

Vibrations in deep drilling systems lead to efficiency deterioration and may even cause the system failure. In this paper, a controller is designed aiming at mitigation of these vibrations, which is based on a neutral-type time delay model that represents distributed axial and torsional dynamics. First, the stability of the associated linearized dynamics is analyzed using a spectral approach. Furthermore, the open-loop system is shown to be stabilizable by state feedback which supports subsequent controller design. An optimization-based continuous pole placement technique has been employed to design a stabilizing controller, which mitigates steady-state drill-string vibrations. The effectiveness of the controller is shown in a representative case study

Delay-dependent exponential stability of neutral stochastic delay systems (vol 54, pg 147, 2009)

In the above titled paper originally published in vol. 54, no. 1, pp. 147-152) of IEEE Transactions on Automatic Control, there were some typographical errors in inequalities. Corrections are presented here