Work

Deep Learning of Delay-Compensated Backstepping for Reaction–Diffusion PDEs

Year: 2025

Type: article

Abstract: 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.

Source: IEEE Transactions on Automatic Control

DOI: 10.1109/tac.2025.3538755

Authors: Shanshan Wang, Mamadou Diagne, Miroslav Krstić

Institutions: University of Shanghai for Science and Technology, University of California San Diego

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: green