Neural Operators for PDE Backstepping Control of First-Order Hyperbolic PIDE with Recycle and Delay

arXiv:2307.11436v2 Announce Type: replace-cross
Abstract: The recently introduced DeepONet operator-learning framework for PDE control is extended from the results for basic hyperbolic and parabolic PDEs to an advanced hyperbolic class that involves delays on both the state and the system output or input. The PDE backstepping design produces gain functions that are outputs of a nonlinear operator, mapping functions on a spatial domain into functions on a spatial domain, and where this gain-generating operator's inputs are the PDE's coefficients. The …

abstract advanced arxiv basic class control cs.lg cs.sy deeponet delay eess.sy framework input math.ap math.oc operators output replace results state type