Flatness of multi-input control-affine systems linearizable via one-fold prolongation

Florentina Nicolau (1) , Witold Respondek (2)

1 QUARTZ - Laboratoire QUARTZ
2 LMI - Laboratoire de Mathématiques de l'INSA de Rouen Normandie

We study flatness of multi-input control-affine systems. We give a geometric characterization of systems that become static feedback linearizable after an invertible one-fold prolongation of a suitably chosen control. They form a particular class of flat systems. Namely, they are of differential weight n + m + 1, where n is the dimension of the state-space and m is the number of controls. We propose conditions (verifiable by differentiation and algebraic operations) describing that class and provide a system of PDE's giving all minimal flat outputs. We illustrate our results by an example of the quadrotor helicopter.

Mots clés: flatness; flat outputs; differential weight; linearization

Domaines: Optimisation et contrôle [math.OC]

Florentina Nicolau, Witold Respondek. Flatness of multi-input control-affine systems linearizable via one-fold prolongation. SIAM Journal on Control and Optimization, In press, ⟨10.1137/140999463⟩. ⟨hal-01401062⟩