Solving Lur'e equations through zeroing neural networks - Yu He; Xiaojuan Wang; Yafei Tie; Huanqi Yang; Theodore E. Simos; Spyridon D. Mourtas; Vasilios N. Katsikis (Information Sciences, 2025)
Solving Lur'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—ZNNLE and ZNNLE-LQOC—specifically designed to solve the Lur'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'e equations; Singular optimal control; Zeroing neural network