New formulation of predictors for finite-dimensional linear control systems with input delay

Delphine Bresch-Pietri (1) , Christophe Prieur (2) , Emmanuel Trélat (3, 4)

1 CAS - Centre Automatique et Systèmes
2 GIPSA-SYSCO - GIPSA - Systèmes non linéaires et complexité
3 LJLL - Laboratoire Jacques-Louis Lions
4 CaGE - Control And GEometry

This paper focuses on a prediction-based control for linear time invariant systems subject to a constant input delay, also known as the Artstein reduction approach. Standardly, this method consists in considering a predicted delay-free system, on which one can design straightforwardly a stabilizing controller. The resulting controller is then defined through an implicit integral equation, involving both the original system state and past values of the input. We propose here an alternative formulation which allows to write explicitly the Artstein transformation, and thus the corresponding controller, in terms of past values of the state only. This formal explicit formulation is the main contribution of the paper.

Mots clés: Time-delay systems; Finite spectrum assignment; Prediction-based controllers

Domaines: Systèmes et contrôle [cs.SY]

Delphine Bresch-Pietri, Christophe Prieur, Emmanuel Trélat. New formulation of predictors for finite-dimensional linear control systems with input delay. Systems and Control Letters, 2018, 113, pp.9-16. ⟨10.1016/j.sysconle.2017.12.007⟩. ⟨hal-01226598v3⟩