Different ZFs lead to different nets: Examples of Zhang generalized inverse

This paper demonstrates the flexibility of Z-type methodology for generating multiple solution-models of time-varying problems. As a case study with examples, we investigate the solution of time-varying generalized inverse (termed Zhang generalized inverse, ZGI). Specifically, to solve for time-varying left generalized inverse (TVLGI or termed Zhang left generalized inverse, ZLGI), five different effective Z-type models are derived by using different Zhang functions (ZFs) as source of derivations and employing the Z-type model design method. In addition, a clear and direct link between model A and the Getz-Marsden (G-M) dynamic system is discovered; and model B with a linear activation function (AF) array has global exponential convergence. Furthermore, two different AFs are adopted for comparisons and verifications.