Flatness and Optimal Control of Oscillators
06 07 Category : Flatness
Author: Pierre Rouchon, International Journal of Tomography & Statistics, Vol. 6, no S07, 2007
The aim of this paper is to present some recent developments and hints for future researches in control inspired of flatness-based ideas. We explain how explicit trajectory parameterization, a property that is central for flat systems, can be useful for the control of various oscillatory systems (linear, nonlinear, finite and/or infinite dimension) of physical and engineering interests. Such parameterization provide simple algorithms to generate optimal trajectories via exact discretization. Three key examples are detailed: a linearized Schrödinger equation describing the interaction of an electro-magnetic field (the control) with an n-levels quantum system; the heavy chain described by a 1D wave equation; an Euler Bernoulli flexion beam.
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BibTeX:
@Article{,
author = {Pierre Rouchon},
title = {Flatness and Optimal Control of Oscillators},
journal = {International Journal of Tomography & Statistics},
volume = {6},
number = {S07},
pages = {8-14},
year = {2007},
}
The aim of this paper is to present some recent developments and hints for future researches in control inspired of flatness-based ideas. We explain how explicit trajectory parameterization, a property that is central for flat systems, can be useful for the control of various oscillatory systems (linear, nonlinear, finite and/or infinite dimension) of physical and engineering interests. Such parameterization provide simple algorithms to generate optimal trajectories via exact discretization. Three key examples are detailed: a linearized Schrödinger equation describing the interaction of an electro-magnetic field (the control) with an n-levels quantum system; the heavy chain described by a 1D wave equation; an Euler Bernoulli flexion beam.
Download PDF
BibTeX:
@Article{,
author = {Pierre Rouchon},
title = {Flatness and Optimal Control of Oscillators},
journal = {International Journal of Tomography & Statistics},
volume = {6},
number = {S07},
pages = {8-14},
year = {2007},
}