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Philippe Martin | MINES ParisTech, PSL University, Paris, France
Flatness: an overview
A control system is called flat if its solutions can be parameterized by a set of "free" functions and their derivatives. Initially developed for finite-dimension nonlinear systems, flatness can be seen as a notion of equivalence to a trivial system by a so-called endogenous feedback. It provides simple solutions for motion planning as well as for tracking (for instance by dynamic feedback linearization), which are two central problems in control theory. Though this flatness property is very strong, it is interesting in practice as many engineering systems are flat. The idea was later adapted to infinite-dimension control systems, and turned out to be fruitful even in the linear case, for instance for motion planning of partial differential equations with boundary control.