Local Input-to-State Stabilization of 1-D Linear Reaction-Diffusion Equation with Bounded Feedback

Aneel Tanwani (1) , Swann Marx (2) , Christophe Prieur (2)

1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
2 GIPSA-SYSCO - GIPSA - Systèmes non linéaires et complexité

The problem of robust stabilization with bounded feedback control is considered for a scalar reaction-diffusion system with uncertainties in the dynamics. The maximum value of the control input acting on one of the boundary points has to respect a given bound at each time instant. It is shown that, if the initial condition and the disturbance satisfy the certain bounds (computed as a function of the bound imposed on the control input), then the proposed control respects the desired saturation level and renders the closed-loop system locally input-to-state stable, that is, the trajectories with certain bound on the initial condition converge to a ball parameterized by certain norm of the disturbance.

Mots clés: 93D05; 93D09; bounded feedback; Lyapunov methods AMS Classification Codes— 93C20; input-to-state stability; Boundary controlled PDEs

Domaines: Automatique

Aneel Tanwani, Swann Marx, Christophe Prieur. Local Input-to-State Stabilization of 1-D Linear Reaction-Diffusion Equation with Bounded Feedback. MTNS 2018 - 23rd International Symposium on Mathematical Theory of Networks and Systems, Jul 2018, Hong Kong, China. 6p. ⟨hal-01785104⟩