On Barriers in State and Input Constrained Nonlinear Systems

In this paper, the problem of state and input constrained control is addressed, with multidimensional constraints. We obtain a local description of the boundary of the admissible subset of the state space where the state and input constraints can be satisfied \emph{for all times}. This boundary is made of two disjoint parts: the subset of the state constraint boundary on which there are trajectories pointing towards the interior of the admissible set or tangentially to it; and a barrier, namely a semipermeable surface which is constructed via a minimum-like principle.Comment: 36 pages, 8 figures, submitte

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.

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

On constrained continuous-time nonlinear control systems

International audienc

A flatness-based iterative method for reference trajectory generation in constrained NMPC

This paper proposes a novel methodology that combines the differential flatness formalism for trajectory generation of nonlinear systems, and the use of a model predictive control (MPC) strategy for constraint handling. The methodology consists of a trajectory generator that generates a reference trajectory parameterised by splines, and with the property that it satisfies performance objectives. The reference trajectory is generated iteratively in accordance with information received from the MPC formulation. This interplay with MPC guarantees that the trajectory generator receives feedback from present and future constraints for real-time trajectory generation

II. Livres

Anzieu D., Bresson F., Chocholle R., Durandin G., Fraisse P, Gratiot-Alphandéry H., Hiriartborde A.-M., Ledoux V., Lévine J., Piéron Henri, Vautrey P. II. Livres. In: L'année psychologique. 1952 vol. 52, n°2. pp. 652-668