Some new interpretations of controllability and their practical implications

摘要

R.E.Kalman introduced the concept of cotrollability for finite-dimensional linear systems at the beginning of the sixties. It has played since then a key role. A vast literature has been devoted to various extensions to nonlinear and infinite-dimensional systems. We first interpret Kalman's controllability in a new module-theoretic language, which is independent of any distinction between thesystem variables. Its nonlinear extensio leads to the notion of differentially flat systems, which were introduced in 1992 by J.Levine, P.Martin, P.Rouchon, and the author.