Zeroing neural dynamics solving time-variant complex conjugate matrix equation $X(\tau)F(\tau)-A(\tau)\overline{X}(\tau)=C(\tau)$

TL;DR

This paper introduces zeroing neural dynamics (ZND) to solve time-variant complex conjugate matrix equations, extending neural network methods to complex, time-dependent systems with proven convergence and demonstrated effectiveness.

Contribution

The paper develops the first neural network approach for time-variant CCME, including new models Con-CZND1 and Con-CZND2 with theoretical convergence proofs.

Findings

ZND effectively solves time-variant CCME

Models outperform real-field approaches

Numerical experiments validate theoretical results

Abstract

Complex conjugate matrix equations (CCME) are important in computation and antilinear systems. Existing research mainly focuses on the time-invariant version, while studies on the time-variant version and its solution using artificial neural networks are still lacking. This paper introduces zeroing neural dynamics (ZND) to solve the earliest time-variant CCME. Firstly, the vectorization and Kronecker product in the complex field are defined uniformly. Secondly, Con-CZND1 and Con-CZND2 models are proposed, and their convergence and effectiveness are theoretically proved. Thirdly, numerical experiments confirm their effectiveness and highlight their differences. The results show the advantages of ZND in the complex field compared with that in the real field, and further refine the related theory.