On the computation of π\pi-flat outputs for differential-delay systems

We introduce a new definition of $\pi$-flatness for linear differential delay systems with time-varying coefficients. We characterize $\pi$- and $\pi$-0-flat outputs and provide an algorithm to efficiently compute such outputs. We present an academic example of motion planning to discuss the pertinence of the approach.Comment: Minor corrections to fit with the journal versio

Correlator Bank Detection of GW chirps. False-Alarm Probability, Template Density and Thresholds: Behind and Beyond the Minimal-Match Issue

The general problem of computing the false-alarm rate vs. detection-threshold relationship for a bank of correlators is addressed, in the context of maximum-likelihood detection of gravitational waves, with specific reference to chirps from coalescing binary systems. Accurate (lower-bound) approximants for the cumulative distribution of the whole-bank supremum are deduced from a class of Bonferroni-type inequalities. The asymptotic properties of the cumulative distribution are obtained, in the limit where the number of correlators goes to infinity. The validity of numerical simulations made on small-size banks is extended to banks of any size, via a gaussian-correlation inequality. The result is used to estimate the optimum template density, yielding the best tradeoff between computational cost and detection efficiency, in terms of undetected potentially observable sources at a prescribed false-alarm level, for the simplest case of Newtonian chirps.Comment: submitted to Phys. Rev.

Thomas Decomposition and Nonlinear Control Systems

This paper applies the Thomas decomposition technique to nonlinear control systems, in particular to the study of the dependence of the system behavior on parameters. Thomas' algorithm is a symbolic method which splits a given system of nonlinear partial differential equations into a finite family of so-called simple systems which are formally integrable and define a partition of the solution set of the original differential system. Different simple systems of a Thomas decomposition describe different structural behavior of the control system in general. The paper gives an introduction to the Thomas decomposition method and shows how notions such as invertibility, observability and flat outputs can be studied. A Maple implementation of Thomas' algorithm is used to illustrate the techniques on explicit examples

A Novel Signaling Network Essential for Regulating Pseudomonas aeruginosa Biofilm Development

The important human pathogen Pseudomonas aeruginosa has been linked to numerous biofilm-related chronic infections. Here, we demonstrate that biofilm formation following the transition to the surface attached lifestyle is regulated by three previously undescribed two-component systems: BfiSR (PA4196-4197) harboring an RpoD-like domain, an OmpR-like BfmSR (PA4101-4102), and MifSR (PA5511-5512) belonging to the family of NtrC-like transcriptional regulators. These two-component systems become sequentially phosphorylated during biofilm formation. Inactivation of bfiS, bfmR, and mifR arrested biofilm formation at the transition to the irreversible attachment, maturation-1 and -2 stages, respectively, as indicated by analyses of biofilm architecture, and protein and phosphoprotein patterns. Moreover, discontinuation of bfiS, bfmR, and mifR expression in established biofilms resulted in the collapse of biofilms to an earlier developmental stage, indicating a requirement for these regulatory systems for the development and maintenance of normal biofilm architecture. Interestingly, inactivation did not affect planktonic growth, motility, polysaccharide production, or initial attachment. Further, we demonstrate the interdependency of this two-component systems network with GacS (PA0928), which was found to play a dual role in biofilm formation. This work describes a novel signal transduction network regulating committed biofilm developmental steps following attachment, in which phosphorelays and two sigma factor-dependent response regulators appear to be key components of the regulatory machinery that coordinates gene expression during P. aeruginosa biofilm development in response to environmental cues

Control of the Toycopter using a Flat Approximation

This paper considers a helicopter-like setup called the Toycopter. Its particularities reside first in the fact that the toycopter motion is constrained to remain on a sphere and second in the use of a variable rotational speed of the propellers to vary the propeller thrust. A complete model using Lagrangian mechanics is derived. The Toycopter is shown to be non differentially flat. Nevertheless, by neglecting specific cross-couplings, a differentially flat approximation can be generated and used for controller design, provided the controller gains do not exceed certain bounds that are given explicitly. The achieved performance is better than with standard linear controllers, especially during large displacements that induce strong nonlinear gyroscopical forces. The results are illustrated both in simulation and experimentally on the setup