Deep Learning of Delay-Compensated Backstepping for ReactionDiffusion PDEs

• 成果类型: Article
• 署名作者: Wang, Shanshan; Diagne, Mamadou; Krstic, Miroslav
• 署名单位: University of Shanghai for Science & Technology; 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.2025.3538755
• 发表日期: 2025
• 页码: 4209-4216
• 关键词: Kernel; Backstepping; DELAYS; PD control; Partial differential equations; Deep learning; training; Three-dimensional displays; Stability criteria; ELECTRONIC MAIL; delay systems; Distributed parameter systems; Neural Networks; partial differential equation (PDE) backstepping

摘要

With deep neural network approximations of partial differential equation (PDE) backstepping, for each new functional coefficient of the PDE plant, the gains are obtained through a function evaluation. In this article, we expand this framework to control of cascaded PDE systems from distinct classes: a reaction-diffusion plant, which is a parabolic PDE, with input delay, which is a hyperbolic PDE. The DeepONet-approximated nonlinear operator for the control gain is a cascade/composition of the operators defined by one hyperbolic PDE of the Goursat form and one parabolic PDE on a rectangle, both of which are bilinear in their input functions and not explicitly solvable. For the DeepONet-approximated delay-compensated PDE backstepping controller, we guarantee exponential stability in the L-2 norm of the plant state and the H-1 norm of the input delay state.