Conception de contrôleurs événementiels pour certaines classes de systèmes dynamiques

Event-triggered control offers a promising alternative to the classical, resource-consuming, periodic control. It suggests to replace the periodic, high frequency sampling used in the continuous-to-discrete transformations of control signals with aperiodic sampling. A new value of the event-triggered control law is computed only when the system's response is unsatisfactory. The control value is kept constant otherwise. In this thesis, we explore ways to induce fewer updates, and to have longer intervals between two samples. We also seek to make the algorithms that we design more detailed, by describing how to choose or compute the optimal parameters. 
In the linear case, we present a stabilizing algorithm in which we relax the stability conditions on the system's Lyapunov function to produce fewer, sparser updates of the control law. Stability is ensured by maintaining the Lyapunov function below a certain decreasing threshold. The optimal threshold function is derived by solving a maximum generalized eigenvalue problem. This approach is then extended to switched linear systems. We also present a self-triggered version of this algorithm using Newton methods for optimization and root-finding. The reference tracking problem is treated in the event-triggered control framework as well. Finally, in the nonlinear case, due to the difficulty of finding a Lyapunov function, we explore the use of contraction analysis. This approach allows us to describe the nonlinear event-triggered control algorithm more thoroughly than if we had used Lyapunov techniques.

President:

Mr Christophe Prieur (Directeur de recherche - CNRS - Gipsa lab)

Directors:

• Mr Nacim Meslem (Maitre de conférence - Grenoble INP )
• Mme Brigitte Bidégaray-Fesquet (chargé de recherche - Université Grenoble Alpes )

Raporteurs:

• Mr Lionel Rosier (professeur des universités - Ecole des mines de Paris )
• Mr Alexandre Seuret (chargé de recherche - LAAS - CNRS )

Examinators:

• Mme Fatiha Alabau (professeur des universités - Université de Lorraine )
• Mr Mohamed Djemai (professeur des universités - Université de Valenciennes )
• Mr Nicolas Marchand (directeur de recherche - CNRS - Gipsa lab )