New Variant-Parameter ZNN Solutions for Resolving Time-Variant Plural Lyapunov Equation Under Preassigned Time
Jiawei Luo, Hui Yang
Abstract
Zeroing neural networks (ZNNs) are effective ways to resolve time-variant problems such as plural Lyapunov equation. In general, the design convergent parameters (DCPs) of ZNN solutions influence their convergence speed. While previous constant-parameter ZNNs (CP-ZNNs) are fixed or constant, it is impractical because the parameters are time-variant in actual hardware situations. On account of this point, the variant parameter and convergent ZNNs (VPC-ZNNs) have been studied in the area sequently. Although these VPC-ZNNs outperform the CP-ZNNs, their DCPs usually keep growing over time and even become infinitely great finally. But infinitely great parameters are unacceptable for us. Meanwhile the computing resources will be wasted because of the growing the parameters even when the VPC-ZNNs become convergent. Based on these, we propose a hyperbolic tangent-type VP-ZNN (HTVP-ZNN) solution owning preassigned-time convergence to resolve time-variant plural Lyapunov equation in this article. HTVP-ZNN can adjust its DCPs, so that they gradually converge to a constant once HTVP-ZNN is convergent under preassigned time. Preassigned-time convergence of HTVP-ZNN and its upper bound are theoretically investigated. Comparative numerical experiments are provided to substantiate the favorable convergence.