Network-Based Distributed Control of Parabolic PDE Systems Under Non-Collocated Observation

This paper investigates the sampled-data distributed control of parabolic partial differential equation (PDE) systems with non-collocated observation. Both the measurement outputs and control inputs are sampled, and transmitted through a delayed network, leading to the issue of spatiotemporally asynchronous sampled-data. A predictor-based observer is proposed, which achieves non-collocated dynamic feedback control while addressing the network-induced input-delay. Furthermore, the try-once-discard protocol is extended to networked PDE systems for the first time, which results in an impulse sampled-data PDE system. A generalized Halanay inequality is newly proposed to address the spatiotemporally asynchronous sampling, complemented by the Lyapunov–Krasovskii method to establish exponential convergence conditions for closed-loop PDEs. With the help of the $C_{0}$ semigroup theory, the well-posedness analysis of the impulsive sampled-data closed-loop PDEs is given by constructing an inhomogeneous abstract Cauchy problem. Finally, a simulation example verifies the effectiveness of the proposed method.