Creator:
Contributor:
Fliess, Michel - ed. ; Jai, Abdelhaq El - ed.
Title:
Motion planning, equivalence, infinite dimensional systems
Subtitle:
Mathematical Theory of Networks and Systems
Group publication title:
Subject and Keywords:
infinite dimensional control systems ; motion planning ; flatness, absolute equivalence ; Pfaffian systems ; delay systems ; Gevrey functions
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. ; 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. ; 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. ; 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.
Publisher:
Zielona Góra: Uniwersytet Zielonogórski
Date:
Resource Type:
Pages:
Source:
AMCS, volume 11, number 1 (2001) ; click here to follow the link