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A criterion for the differential flatness of a nonlinear control system

Abstract : Let's consider a control system described by the implicit equation F (x, ˙ x) = 0. If this system is differentially flat, then the following criterion is satisfied : For some integer r, there exists a function ϕ(y0, y1, .., yr) satisfying the following conditions: (1) The map (y0, .., yr+1) → (ϕ(y0, y1, .., yr), ∂ϕ/ ∂y0 y1 + ∂ϕ/ ∂y1 y2 + .. + ∂ϕ/ ∂yr yr+1) is a submersion on the variety F (x, p) = 0. (2) The map y0 → x0 = ϕ(y0, 0, .., 0) is a diffeomorphism on the equilibrium variety F (x, 0) = 0. Inversely, if a control system satifies this flatness criterion, then it is locally controllable at equilibrium points.
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https://hal-mines-paristech.archives-ouvertes.fr/hal-01631061
Contributor : Bruno Sauvalle <>
Submitted on : Thursday, November 9, 2017 - 4:19:06 PM
Last modification on : Tuesday, July 21, 2020 - 3:17:42 AM
Long-term archiving on: : Saturday, February 10, 2018 - 3:04:22 PM

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  • HAL Id : hal-01631061, version 1
  • ARXIV : 1711.04995

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Bruno Sauvalle. A criterion for the differential flatness of a nonlinear control system. 2017. ⟨hal-01631061⟩

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