In-domain stabilization of block diagonal infinite-dimensional systems with time-varying input delays

Hugo Lhachemi (1, 2) , Christophe Prieur (3) , Robert Shorten (4)

1 L2S - Laboratoire des signaux et systèmes
2 CentraleSupélec
3 GIPSA-INFINITY - GIPSA - Infinite Dimensional Dynamics
4 Imperial College London

This paper is concerned with the in-domain stabilization of a class of block diagonal infinite-dimensional systems in the presence of an uncertain and time-varying delay in the distributed control input. Two actuation schemes are considered. The first one assumes a control input that is fully distributed over the domain. The second one assumes that the control input is finite-dimensional, acting over the domain via a bounded operator. In both cases, the control design strategy consists in a predictor feedback law synthesized on a finite-dimensional truncated LTI model capturing the unstable dynamics of the original infinitedimensional system. The predictor feedback law is designed based on the knowledge of the nominal value of the uncertain and time-varying input delay. In the second actuation scheme, the case of distinct input delays in the different scalar control input channels is considered. Index Terms-Delayed distributed actuation, partial differential equations, predictor feedback law. H. Lhachemi and R. Shorten acknowledge the support of Science Foundation Ireland (Grant numbers 16/RC/3872 and 16/IA/4610) and I-Form industry partners. C. Prieur acknowledges the support from MIAI@Grenoble Alpes, (ANR-19-P3IA-0003).

Mots clés: Delayed distributed actuation; partial differential equations; predictor feedback law

Domaines: Optimisation et contrôle [math.OC]; Systèmes et contrôle [cs.SY]

Hugo Lhachemi, Christophe Prieur, Robert Shorten. In-domain stabilization of block diagonal infinite-dimensional systems with time-varying input delays. IEEE Transactions on Automatic Control, 2021, 66 (12), pp.6017-6024. ⟨10.1109/TAC.2021.3059103⟩. ⟨hal-03147533⟩