TY - GEN
A1 - Rouchon, Pierre
A2 - Fliess, Michel - ed.
A2 - Jai, Abdelhaq El - ed.
PB - Zielona Góra: Uniwersytet Zielonogórski
N2 - 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.
N2 - 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.
N2 - 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.
N2 - 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.
L1 - http://zbc.uz.zgora.pl/Content/58760/AMCS_2001_11_1_7.pdf
L2 - http://zbc.uz.zgora.pl/Content/58760
KW - infinite dimensional control systems
KW - motion planning
KW - flatness, absolute equivalence
KW - Pfaffian systems
KW - delay systems
KW - Gevrey functions
T1 - Motion planning, equivalence, infinite dimensional systems
UR - http://zbc.uz.zgora.pl/dlibra/docmetadata?id=58760
ER -