Network-Based Distributed Control of Parabolic PDE Systems Under Noncollocated Observation

This article investigates the sampled-data distributed control of parabolic partial differential equation (PDE) systems with noncollocated 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 noncollocated 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$C_{0}$</tex-math></inline-formula> 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.