@article {HE2025122418,
	title = {Solving Lur{\textquoteright}e equations through zeroing neural networks},
	journal = {Information Sciences},
	volume = {718},
	year = {2025},
	pages = {122418},
	abstract = {Solving Lur{\textquoteright}e equations plays a critical role in addressing linear-quadratic optimal control (LQOC) problems, especially in cases where the control cost matrices are singular. This paper introduces, for the first time, two novel zeroing neural network (ZNN) models{\textemdash}ZNNLE and ZNNLE-LQOC{\textemdash}specifically designed to solve the Lur{\textquoteright}e equation system and the LQOC problem, respectively. The proposed models extend the applicability of the ZNN methodology to these challenging scenarios by offering robust and efficient solutions to time-varying matrix equations. Theoretical analyses confirm the validity of both models, while numerical simulations and practical applications demonstrate their effectiveness. Moreover, a comparative study with an enhanced alternating-direction implicit (ADI) method highlights the superior performance of the ZNNLE-LQOC model in solving LQOC problems.},
	keywords = {Dynamic system, Linear-quadratic optimal control, Lur{\textquoteright}e equations, Singular optimal control, Zeroing neural network},
	issn = {0020-0255},
	doi = {https://doi.org/10.1016/j.ins.2025.122418},
	url = {https://www.sciencedirect.com/science/article/pii/S002002552500550X},
	author = {Yu He and Xiaojuan Wang and Yafei Tie and Huanqi Yang and Theodore E. Simos and Spyridon D. Mourtas and Vasilios N. Katsikis}
}
