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.

/pdf/flatness-and-defect-of-non-linear-systems-introductory-42ot9eoqmh.pdf

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)

Stabilization of st venant equations using riemann invariants: application to waterways with mobile spillways

A Lyapunov Approach for the Control of Multi Reach Channels Modelled by Saint-Venant Equations

In this paper, we shall deal with the control of fedbatch fermentation processes exhibiting substrate inhibition phenumenons. A simple adaptive control scheme based on the nonlinear structure of the system is proposed. It is shown how this adaptive controller can contribute to optimize the process yield without the knowledge of the process kinetics being necessary.

Adaptive-control of Fedbatch Bioreactors

Output feedback control of food-chain systems

https://perso.uclouvain.be/georges.bastin/paper60.pdf

Georges Bastin

Papers

Stabilization of st venant equations using riemann invariants: application to waterways with mobile spillways

A Lyapunov Approach for the Control of Multi Reach Channels Modelled by Saint-Venant Equations

Adaptive-control of Fedbatch Bioreactors

Output feedback control of food-chain systems

Brief An estimator of the inverse covariance matrix and its application to ML parameter estimation in dynamical systems