@misc{Rouchon_Pierre_Motion,
 author={Rouchon, Pierre},
 howpublished={online},
 publisher={Zielona Góra: Uniwersytet Zielonogórski},
 language={eng},
 abstract={Motion planning, i.e., steering a system from one state to another, is a basic question in automatic control. For a certain class of systems described by ordinary differential equations and called flat systems (Fliess et al., 1995; 1999a), motion planning admits simple and explicit solutions.},
 abstract={This stems from an explicit description of the trajectories by an arbitrary time function y, the flat output, and a finite number of its time derivatives. Such explicit descriptions are related to old problems on Monge equations and equivalence investigated by Hilbert and Cartan.},
 abstract={The study of several examples (the car with n-trailers and the non-holonomic snake, pendulums in series and the heavy chain, the heat equation and the Euler-Bernoulli exible beam) indicates that the notion of flatness and its underlying explicit description can be extended to infinite-dimensional systems.},
 abstract={As in the finite-dimensional case, this property yields simple motion planning algorithms via operators of compact support. For the non-holonomic snake, such operators involve non-linear delays. For the heavy chain, they are defined via distributed delays. For heat and Euler-Bernoulli systems, their supports are reduced to a point and their definition domain coincides with the set of Gevrey functions of order 2.},
 type={artykuł},
 title={Motion planning, equivalence, infinite dimensional systems},
 keywords={infinite dimensional control systems, motion planning, flatness, absolute equivalence, Pfaffian systems, delay systems, Gevrey functions},
}