Discrete-time Zhang neural network of O(τ3) pattern for time-varying matrix pseudoinversion with application to manipulator motion generation

In addition to the high-speed parallel-distributed processing property, neural networks can be readily implemented by hardware and thus have been applied widely in various fields. In this paper, via a new numerical-differentiation formula, two Taylor-type discrete-time Zhang neural network (ZNN) models (termed T-ZNN-K and T-ZNN-U models) are first proposed, developed and investigated for online time-varying matrix pseudoinversion. For comparison as well as for illustration, Euler-type discrete-time ZNN models (termed E-ZNN-K and E-ZNN-U models) and Newton iteration are presented. In addition, according to the criterion of whether the time-derivative information of time-varying matrix is explicitly known or not, these discrete-time ZNN models are classified into two categories: (1) models with time-derivative information known (i.e., T-ZNN-K and E-ZNN-K models), and (2) models with time-derivative information unknown (i.e., T-ZNN-U and E-ZNN-U models). Moreover, theoretical analyses show that, the maximal steady-state residual errors (MSSREs) of T-ZNN-K and T-ZNN-U models have an O(tau(3)) pattern, the MSSREs of E-ZNN-K and E-ZNN-U models have an O(tau(2)) pattern, whereas the MSSRE of Newton iteration has an O(tau) pattern, with tau denoting the sampling gap. Finally, two illustrative numerical experiments and an application example to manipulator motion generation are provided and analyzed to substantiate the efficacy of the proposed Taylor-type discrete-time ZNN models for online time-varying matrix pseudoinversion. (C) 2014 Elsevier B.V. All rights reserved.