Interval estimation for second-order delay differential equations with delayed measurements and uncertainties

Tatiana Kharkovskaia (1) , Denis Efimov (1) , Emilia Fridman (2) , Andrey Polyakov (3, 1) , Jean-Pierre Richard (1)

1 NON-A-POST - Non-Asymptotic estimation for online systems
2 Department of Electrical Engineering
3 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189

The interval estimation design is studied for a second-order delay differential equation with position delayed measurements, uncertain input and initial conditions. The proposed method contains two consecutive interval observers. The first one estimates the interval of admissible values for the position without delay for each instant of time using new delay-dependent conditions on positivity. Then derived interval estimates of the position are used to design the second observer estimating an interval of admissible values for the velocity of the considered dynamical system. The results are illustrated by numerical experiments for an example.

Domaines: Automatique / Robotique

Tatiana Kharkovskaia, Denis Efimov, Emilia Fridman, Andrey Polyakov, Jean-Pierre Richard. Interval estimation for second-order delay differential equations with delayed measurements and uncertainties. CDC 2018 - 57th IEEE Conference on Decision and Control, Dec 2018, Fontainebleau (FL), United States. ⟨hal-01888545⟩