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Fliess, Michel; Lévine, Jean; Martin, Philippe; Rouchon, Pierre

Flatness and defect of non-linear systems: Introductory theory and examples. (English) Zbl 0838.93022

Int. J. Control 61, No. 6, 1327-1361 (1995).
Flat systems form a class of nonlinear systems which can be transformed, via a certain feedback design, to one which is equivalent to a linear system. Once this is done, the resulting system is subject to the tools available for linearizable systems. The concrete expression of the transformation allows to invert the schemes and interpret them in terms of the original system parameters. The beautifully crafted paper under review introduces this theory by analyzing in detail several case studies, along with the relevant abstract theory. The latter includes the algebraic framework of differential fields, their modules and ideals.
The defect of a differential field is an integer which measures, roughly, how close to a controllable linear system the original systems can be transformed. A flat system is one whose defect is zero. The paper exhibits examples for flat systems, which include the two-dimensional crane and a car with several trailers. Parking the car when there are two trailers is demonstrated in detail, including a reference for a numerical scheme. It is also shown how a non-flat system may be transformed into a flat one using high-frequeny control; this is demonstrated on a variable length pendulum.
Reviewer: Z.Artstein (Rehovot)

Cited in 4 Reviews
Cited in 313 Documents

MSC:

93B25 Algebraic methods
93B18 Linearizations
93C10 Nonlinear systems in control theory

Keywords:

flat systems; nonlinear; differential fields; modules; defect
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References:

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