An Arctan-Type Varying-Parameter ZNN for Solving Time-Varying Complex Sylvester Equations in Finite Time

Zeroing neural network (ZNN) is an effective neural solution to time-varying problems, including time-varying complex Sylvester equations. Generally, a ZNN model involves a convergence design parameter (CDP) that influences its convergence rate. In traditional fixed-parameter ZNNs (FP-ZNNs), the CDPs are set to be constant, which is not realistic since the CDPs are actually time-varying in practical hardware environments. By considering this fact, varying-parameter ZNNs (VP-ZNNs) with time-varying CDPs have been researched in the literature. Although these VP-ZNNs have been demonstrated to deliver superior convergence as compared with FP-ZNNs, they have one drawback, that is, their CDPs usually keep increasing with time, meaning that the CDPs tend to be infinity large with time progresses. Evidently, infinity large CDPs are unacceptable in practice. Moreover, computing resources will be wasted by growing the CDPs with time after the VP-ZNNs become convergent. To tackle the above issues, this article, for the first time, proposes an arctan-type VP-ZNN (ATVP-ZNN) with finite-time convergence for solving time-varying complex Sylvester equations. The ATVP-ZNN is able to adjust its CDPs that finally converge to be constant when the ATVP-ZNN becomes convergent in finite time. In theory, the finite-time convergence of the ATVP-ZNN and the upper bound of the CDPs are mathematically analyzed. Numerical studies are comparatively performed with the superior convergence of the ATVP-ZNN substantiated.

Automated summary

This article proposes an arctan-type varying-parameter neural network (ATVP-ZNN) with finite-time convergence for solving time-varying complex Sylvester equations. Theoretical analysis and numerical studies demonstrate the superior convergence of ATVP-ZNN.