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

We introduce flat systems, which are equivalent to linear ones via a special type of feedback called endogenous. Their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of Kalman's controllability. The distance to flatness is measured by a non-negative integer, the defect. We utilize differential algebra where flatness- and defect are best defined without distinguishing between input, state, output and other variables. Many realistic classes of examples are flat. We treat two popular ones: the crane and the car with n trailers, the motion planning of which is obtained via elementary properties of plane curves. The three non-flat examples, the simple, double and variable length pendulums, are borrowed from non-linear physics. A high frequency control strategy is proposed such that the averaged systems become flat.

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Flatness and defect of non-linear systems: introductory theory and examples

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).

The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

Sur la mod´elisation et le contrˆole des r´eseaux dynamiques conservatifs Georges Bastin1 1 CESAME, Universit´e Catholique de Louvain 4, avenue G. Lemaˆitre, 1348 Louvain-la-Neuve, Belgique (bastin@inma.ucl.ac.be) R´esum´e—Un premier objectif de cette communication est de pr´esenter les principes g´en´eraux qui pr´esident `a la mise en ´equation des mod`eles dynamiques des r´eseaux conservatifs, aussi bien dans le cas des mod`eles en dimension ﬁnie que dans celui des mod`eles en dimension inﬁnie. Un deuxi`eme objectif est de pr´esenter deux questions relatives au contrˆole en boucle ferm´ee de ces r´eseaux : d’une part, le contrˆole de congestion pour les mod`eles de r´eseaux en dimension ﬁnie ; d’autre part, la stabilisation en boucle ferm´ee des ´etats de r´egime permanent pour les mod`eles de r´eseaux en dimension inﬁnie. Mots-cl´es—R´eseaux, lois de conservation, contrˆole de conges- tion, stabilisation, compartiments. I. Introduction Les r´eseaux dynamiques consid´er´es dans cet article sont pr´esents dans de tr`es nombreuses applications actuelles de la technologie et de la science du contrˆole. Les applications auxquelles je me

Sur la modélisation et le contrôle des réseaux dynamiques conservatifs

Identification of a Bio-Methanization Process: A Case Study

In this paper, a continuous-time non linear adaptive controller is designed for the regulation of the substrate concentration of non linear fermentation processes. The design is based on a time varying non linear model obtained from material balance equations. The convergence and the stability of the algorithm are demonstrated, using Liapunov's techniques, both in the deterministic case and in the bounded disturbance case.

Stability and convergence analysis of a continuous-time adaptive control algorithm for fermentation processes

Robustness of Adaptive Observers for Time Varying Systems

RÉSUMÉ.On considère un bief de canal d’irrigation incliné, soumis à un prélèveme nt d’eau, dont la dynamique est décrite par les équations de Saint-Venant. On prop ose une loi de commande par amortissement frontière ayant pour objectif de stabiliser le nive au et le débit autour d’un profil d’équilibre désiré. La convergence de l’algorithme de con trôle est analysée à l’aide des solutions caractéristiques. La performance du contrôle est illustrée p ar des simulations réalistes. Une version adaptative du contrôle est proposée dans le cas o ù le prélèvements sont inconnus.

Georges Bastin

Papers

Sur la modélisation et le contrôle des réseaux dynamiques conservatifs

Identification of a Bio-Methanization Process: A Case Study

Stability and convergence analysis of a continuous-time adaptive control algorithm for fermentation processes

Robustness of Adaptive Observers for Time Varying Systems

Commande frontière adaptative d'un bief de canal avec prélèvements inconnus