There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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Convex Analysisの二,三の進展について

to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解

Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)

Construction and dissemination of information veracity on French social media during crises: Comparison of Twitter and Wikipedia

Control theory has significantly evolved in the field of the nonlinear control. However, the methods used in the aerospace industry lie usually on linear techniques applied to linearized models. The increasing requirements in terms of operational reliability and performance ask for the development of new control techniques more complex in order to meet the new demands. Therefore, the industry is moving to the modern control theory looking for new nonlinear approaches. In particular, actuators saturation represents a nonlinear phenomenon common in almost all physical applications. This can then lead to performance degradation, limit cycle appearance, non-desired equilibrium conditions, and even system instability. The objective of this chapter is to adapt and develop the anti-windup compensator design to the control with high precision for the angular and the linear axes of a satellite. In the aerospace application field, this situation meets with the drag-free or the formation flying missions. These missions use high-precision thrusters as actuators whose capacity appears to be critically low. Moreover, thrusters have a particular modeling. Allocation functions adapted to the anti-windup design are then explored. In addition considering the current state of the art of the anti-windup design, there is a strong necessity of using symmetrizing techniques for the saturation. The main objective of this work consists in applying the developed tools on an aerospace study case. As an example, a complete methodology is proposed to control a formation flying mission controlling both attitude and relative position.

/pdf/formation-flying-control-for-satellites-anti-windup-based-eusgear119.pdf

Formation Flying Control for Satellites: Anti-windup Based Approach

Design of saturated controls for an unstable parabolic PDE

In this chapter, we address the problem of the dynamic boundary stabilization of linear, quasilinear and LPV first-order hyperbolic systems. We provide sufficient conditions for the exponential stability for this class of infinite dimensional systems by means of Lyapunov based techniques and matrix inequalities. We develop an applicative example of a temperature boundary control in a Poiseuille flow using some of our main results and we present simulation results that illustrate the efficiency of our approach.

/pdf/dynamic-boundary-stabilization-of-first-order-hyperbolic-3miiks7kff.pdf

Dynamic Boundary Stabilization of First Order Hyperbolic Systems

The paper addresses the problem of characterizing and computing an estimation of the basin of attraction for saturated hybrid systems. Hybrid systems presenting saturation on signals involved in both the continuous-time and the discrete-time dynamics are considered. A geometrical characterization of local convergence is provided and employed to extend results proper of continuous-time and discrete-time saturated systems to the hybrid ones. A computation oriented condition of local convergence is given in form of convex constraints.

/pdf/ellipsoidal-invariant-sets-for-saturated-hybrid-systems-x3bwbiieum.pdf

Christophe Prieur

Papers

Construction and dissemination of information veracity on French social media during crises: Comparison of Twitter and Wikipedia

Formation Flying Control for Satellites: Anti-windup Based Approach

Design of saturated controls for an unstable parabolic PDE

Dynamic Boundary Stabilization of First Order Hyperbolic Systems

Ellipsoidal invariant sets for saturated hybrid systems