Inverse-Free Discrete ZNN Models Solving for Future Matrix Pseudoinverse via Combination of Extrapolation and ZeaD Formulas

Abstract

Time-varying matrix pseudoinverse (TVMP) problem has been investigated by many researchers in recent years, but a new class of matrix termed Zhang matrix has been found and not been handled by some conventional models, e.g., Getz–Marsden dynamic model. On the other way, future matrix pseudoinverse (FMP), as a more challenging and intractable discrete-time problem, deserves more attention due to its significant role-playing on some engineering applications, such as redundant manipulator. Based on the zeroing neural network (ZNN), this article concentrates on designing new discrete ZNN models appropriately for computing the FMPs of all matrices of full rank, including the Zhang matrix. First, an inverse-free continuous ZNN model for computing TVMP is derived. Subsequently, Zhang et al. discretization (ZeaD) formulas and equidistant extrapolation formulas are used to discretize the continuous ZNN model to two discrete ZNN models for computing FMPs with different truncation errors. The numerical experiments are conducted for the five conventional discrete models and two new discrete ZNN models. Distinct numerical results substantiate the effectiveness and choiceness of newly proposed models. Finally, one of the newly proposed models is implemented on simulating and physical instances of robot manipulators, respectively, to show its practicability.