Level-2 Discrete Noninverse Zeroing Neuronet Algorithm Tackling Future Matrix-Vector Linear Equations Problem With Applications.

Forecasting future unknown information of the future matrix-vector linear equations (FMVLEs) by utilizing only current and historical known information is a challenging and crucial problem. In this article, the FMVLE problem is first reformulated as a future output-zeroing problem. By developing a level-2 control method and incorporating a discretization technique, a brand-new level-2 discrete noninverse zeroing neuronet (L2-DNIZN) algorithm is proposed. The proposed L2-DNIZN algorithm eliminates the complicated time-varying matrix inversion (TVMI) computation, thereby markedly decreasing computational complexity. Moreover, the proposed algorithm addresses the FMVLE and future output-zeroing problems from the level-2 control perspective, successfully enhancing computational accuracy. Theoretical analyses show the convergence properties of the L2-DNIZN algorithm. Additionally, numerical and comparative experiments are provided to substantiate the efficacy, robustness, and superiority of the L2-DNIZN algorithm. Finally, the L2-DNIZN algorithm efficiently and rapidly tackles the mobile target (MT) positioning and Kinova Gen3 robotic arm pose control problems, validating its practicality and applicability.