Neural Operator Feedback for a First-Order PIDE With Spatially Varying State Delay
成果类型：
Article
署名作者：
Qi, Jie; Hu, Jiaqi; Zhang, Jing; Krstic, Miroslav
署名单位：
Shanghai Maritime University; University of California System; University of California San Diego
刊物名称：
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
ISSN/ISSBN：
0018-9286
DOI：
10.1109/TAC.2025.3614407
发表日期：
2026
关键词：
摘要：
A transport PDE with a spatial integral and recirculation with constant delay has been a benchmark for neural operator (NO) approximations of PDE backstepping controllers. Introducing a spatially varying delay into the model gives rise to a gain operator defined through integral equations which the operator's input-the varying delay function-enters in previously unencountered manners, including in the limits of integration and as the inverse of the delayED time function. This, in turn, introduces novel mathematical challenges in estimating the operator's Lipschitz constant. The backstepping kernel function having two branches endows the feedback law with a two-branch structure, where only one of the two feedback branches depends on both of the kernel branches. For this rich feedback structure, we propose a NO approximation of such a two-branch feedback law and prove the approximator to be semiglobally practically stabilizing. With numerical results we illustrate the training of the NO and its stabilizing capability.