Solving for ZGI via ZNN and discrete-time algorithms with application to robot control

In this paper, by defining different error functions, two continuous-time models of Zhang neural net (ZNN) termed the ZNN-I and ZNN-II models are developed and investigated to solve for time-varying generalized inverse (i.e., Zhang generalized inverse, ZGI). In addition, comparing the ZNN models with the dynamic system proposed by Getz and Marsden (G-M), we show that such a G-M dynamic system can also be derived from the ZNN models. For the purpose of potential hardware (e.g., digital circuit or computer) implementation, the discrete-time algorithms (depicted by systems of difference equations) of the presented ZNN-I model are proposed and investigated in two situations, i.e., the time-derivative of the time-varying coefficient matrix being known and unknown. Simulative and numerical results further demonstrate the efficacy of the presented ZNN models for ZGI solving. Moreover, these ZNN models are applied to the kinematic control of a three-link planar robot manipulator via computing ZGI, showing their application prospects.