Neural operators for PDE backstepping control of first-order hyperbolic PIDE with recycle and delay

被引:6
|
作者
Qi, Jie [1 ,2 ,4 ]
Zhang, Jing [1 ]
Krstic, Miroslav [3 ]
机构
[1] Donghua Univ, Coll Informat Sci & Technol, Shanghai 201620, Peoples R China
[2] Donghua Univ, Engn Res Ctr Digitized Text & Fash Technol, Minist Educ, Shanghai 201620, Peoples R China
[3] Univ Calif San Diego, Dept Mech & Aerosp Engn, La Jolla, CA 92093 USA
[4] Bldg 2,2999 North Renmin Rd, Shanghai, Peoples R China
基金
中国国家自然科学基金;
关键词
First-order hyperbolic partial integral; differential equation; PDE backstepping; DeepONet; Delays; Learning-based control; LINEAR-QUADRATIC REGULATOR; BOUNDARY CONTROL; GRADIENT METHODS; STABILIZATION; SYSTEMS; TRACKING;
D O I
10.1016/j.sysconle.2024.105714
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
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 operator is approximated with a DeepONet neural network to a degree of accuracy that is provably arbitrarily tight. Once we produce this approximationtheoretic result in infinite dimension, with it we establish stability in closed loop under feedback that employs approximate gains. In addition to supplying such results under full -state feedback, we also develop DeepONetapproximated observers and output -feedback laws and prove their own stabilizing properties under neural operator approximations. With numerical simulations we illustrate the theoretical results and quantify the numerical effort savings, which are of two orders of magnitude, thanks to replacing the numerical PDE solving with the DeepONet.
引用
收藏
页数:16
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