Output feedback stabilization of reaction–diffusion PDEs with a non-collocated boundary condition

Hugo Lhachemi (1) , Christophe Prieur (2)

1 L2S - Laboratoire des signaux et systèmes
2 GIPSA-INFINITY - GIPSA - Infinite Dimensional Dynamics

This paper addresses the control design problem of output feedback stabilization of a reactiondiffusion PDE with a non-collocated boundary condition. More precisely, we consider a reactiondiffusion equation with a boundary condition describing a proportional relationship between the left and right Dirichlet traces. Such a boundary condition naturally emerges, e.g., in the context of reaction-diffusion partial differential equations presenting a transport term and with a periodic Dirichlet boundary condition. The control input takes the form of the left Neumann trace. Finally, the measurement is selected as a pointwise Dirichlet measurement located either in the domain or at the boundary. The adopted control strategy takes the form of a finite-dimensional controller coupling a state feedback and a finite-dimensional observer. The stability of the closed-loop system is obtained provided the order of the observer is selected to be large enough. Finally, we extend this result to the establishment of an input-to-state stability estimate with respect to an additive perturbation in the application of the boundary control.

Mots clés: Reaction–diffusion PDEs; Non-collocated boundary conditions; Output feedback; Finite-dimensional control

Domaines: Automatique / Robotique

Hugo Lhachemi, Christophe Prieur. Output feedback stabilization of reaction–diffusion PDEs with a non-collocated boundary condition. Systems and Control Letters, 2022, 164 (june), pp.105238. ⟨10.1016/j.sysconle.2022.105238⟩. ⟨hal-03665170⟩