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)

Modelling, simulation and control of the traffic at the terminus stations of urban underground railway lines

Identification of a Reaction Mechanism for a Class of Animal Cell Cultures

A discrete time self tuning computed torque controller is designed for robotic manipulators with unknown physical parameters. It is based on two "exact" discrete ZOH models of manipulators. The first one is linear in the parameters and is used as a basis for on line parameter estimation. The second one is linear analytic and is used for the design of a "Predictive controller".

A discrete time self tuning computed torque controller for robotic manipulators

The cement milling circuit can be seen as a two inputs/two outputs system. The designed multivariable control is based on a LQ controller and a Kalman filter. The authors' main goal is to choose the four design parameters (two diagonal weighting matrices) in order to achieve good performances in terms of rise time, deviation and overshoot. The authors have experimented with several selection methods. The paper compares different approaches and shows the latest developments concerning the best of them.

Georges Bastin

Papers

Modelling, simulation and control of the traffic at the terminus stations of urban underground railway lines

Identification of a Reaction Mechanism for a Class of Animal Cell Cultures

A discrete time self tuning computed torque controller for robotic manipulators

Cement mill optimization: design parameters selection of the LQG controller

Robust global state feedback stabilization of cement mills