Flatness and Optimal Control of Oscillators
Résumé
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.