Méthodes ensemblistes pour la commande des sytèmes affectés par retard variable. Application pour la commande des systèmes en réseau.

摘要

We considered the process regulation which is based on feedback affected by varying delays. Proposed approach relies on set-based control methods. One part of the thesis examines active control design for compensation of delays in sensor-to controller communication channel. This problem is regarded in a general perspective of the fault tolerant control where delays are considered as a particular degradation mode of the sensor. Obtained results are also adapted to the systems with redundant sensing elements that are prone to abrupt faults. In this sense, an unified framework is proposed in order to address the control design with outdated measurements provided by unreliable sensors.Positive invariance for linear discrete-time systems with delays is outlined in the second part of the thesis. Concerning this class of dynamics, there are two main approaches which define positive invariance. The first one relies on rewriting a delay-difference equation in the augmented state-space and applying standard analysis and control design tools for the linear systems. The second approach considers invariance in the initial state-space. However, the initial state-space characterization is still an open problem even for the linear case and it represents our main subject of interest. As a contribution, we provide new insights on the existence of the positively invariant sets in the initial state-space. Moreover, a construction algorithm for the minimal robust D-invariant set is outlined. Additionally, alternative invariance concepts are discussed.