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Flatness and Optimal Control of Oscillators

Abstract : 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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https://hal-mines-paristech.archives-ouvertes.fr/hal-00516682
Contributor : François Chaplais <>
Submitted on : Friday, September 10, 2010 - 4:16:43 PM
Last modification on : Tuesday, June 1, 2021 - 10:52:06 PM

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  • HAL Id : hal-00516682, version 1

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Pierre Rouchon. Flatness and Optimal Control of Oscillators. International Journal of Tomography and Statistics, Indian Society for Development and Environment Research, 2007, 6 (S07), pp.8-14. ⟨hal-00516682⟩

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