GMDS-ZNN Model 3 and its Ten-Instant Discrete Algorithm for Time-Variant Matrix Inversion Compared With Other Multiple-Instant Ones

Abstract

The online time-variant matrix inversion problem has attracted extensive attention and study, because of its considerable appearance and application in scientific research and industrial production. For various control optimization problems, the demand for the high-precision and rapid-convergence of matrix inversion algorithm is increasing. It remains an ongoing challenge due to the rigorous requirements of precision and convergence of the algorithm. In this paper, on the basis of our previous works, by using Zhang neural network (ZNN) method, a continuous time-variant matrix inversion model, which is also a Getz-Marsden dynamic system (i.e., GMDS-ZNN model 3), is proposed. Besides, a general ten-instant Zhang et al discretization (ZeaD) formula is presented and investigated, with corresponding theoretical results being provided. Next, by applying this general formula to discretize the continuous time-variant matrix inversion model, a general ten-instant discrete time-variant matrix inversion (DTVMI) algorithm with the sixth-order precision is proposed. For comparison, four other DTVMI algorithms, with the second-, third-, fourth-, and fifth-order precisions, are also proposed and presented, respectively, by using other ZeaD formulas to discretize the continuous time-variant matrix inversion model. Besides, for the situation of coefficient matrix derivative being unknown, we provided the formula of estimating it with the fifth-order precision. With the help of the proposed matrix derivative estimation formula, the actual application field of GMDS-ZNN model 3 is expanded evidently. Finally, theoretical analyses and simulation experiment results highlight the effectiveness and accuracy of the proposed GMDS-ZNN model 3 and DTVMI algorithms.