The prescribed-time neurodynamic approaches for solving time-varying absolute value equations

In this paper, we consider time-varying absolute value equations (TVAVEs). Incorporating the advantages of zeroing neurodynamic approaches (ZNA) and prescribed-time convergence, a novel prescribed-time robust zeroing neurodynamic approach (PTRZNA) is proposed for solving TVAVEs. Through rigorous theoretical analysis, it is proved that PTRZNA can not only tackle with TVAVEs in prescribed time, but also is independent of the initial conditions. In addition, PTRZNA is tolerant to any bounded noise. By introducing adaptive parameters and robust design, the prescribed-time gradient neurodynamic approach (PTGNA) is proposed. Theoretical analysis indicates that PTGNA can achieve convergence within the prescribed time and is robust to bounded vanishing noise and bounded non-vanishing noise. Furthermore, PTGNA can effectively solve TVAVEs in an inverse-free manner. Numerical simulations are given to demonstrate the effectiveness of the proposed PTRZNA and PTGNA.