Some new interpretations of controllability and their practical implicat ions`

摘要

R.E. Kalman introduced the concept of controllability for finite-dimensional linear systems at the beginning of the sixties. It has played since then a key role. A vast liter- ature has been devoted to various extensions to nonlin- ear and infinite-dimensional systems. We first interpret Kalman's controllability in a new module-theoretic lan- guage, which is independent of any distinction between the system variables. lts nonlinear extension leads to the notion of differentially flat systems, which were introduced in 1992 by J. Levine, P. Martin, P. Rouchon, and the au- thor. They permit a straightforward trajectory tracking, which has been illustrated by numerous applications. In 1995 H. Mounier worked out the case of linear delay sys- tems and discovered a new type of controllability which is verified bv most realistic case-studies. We will con- clude with some examples of systems governed by partial differential equations, which were recently studied by H. Mounier, P. Rouchon, J. Rudolph, and the author.