Hyperbolic Tangent-Type Variant-Parameter and Robust ZNN Solutions for Resolving Time-Variant Sylvester Equation in Preassigned-Time

Abstract

To solve a general time-variant Sylvester equation, two novel zeroing neural networks (ZNNs) solutions are designed and analyzed. In the foregoing ZNN solutions, the design convergent parameters (CPs) before the nonlinear stimulated functions are very pivotal because CPs basically decide the convergent speeds. Nonetheless, the CPs are generally set to be constants, which is not feasible because CPs are generally time-variant in practical hardware conditions particularly when the external noises invade. So, a lot of variant-parameter ZNNs (VP-ZNNs) with time-variant CPs have been come up with. Comparing with fixed-parameter ZNNs, the foregoing VP-ZNNs have been illustrated to own better convergence, the downside is that the CPs generally increases over time, and will be probably infinite at last. Obviously, infinite large CPs would lead to be non-robustness of the ZNN schemes, which are not permitted in reality when the exterior noises inject. Moreover, even though VP-ZNNs are convergent over time, the growth of CPs will waste tremendous computing resources. Based on these factors, 2 hyperbolic tangent-type variant-parameter robust ZNNs (HTVPR-ZNNs) have been proposed in this paper. Both the convergent preassigned-time of the HTVPR-ZNN and top-time boundary of CPs are theoretically investigated. Many numerical simulations substantiated the admirable validity of the HTVPR-ZNN solutions.