A fast-convergent zeroing neural network for solving time-varying full-rank Moore–Penrose inverse

Purpose To improve convergence speed and accuracy in computing the Moore–Penrose inverse (MPI) of time-varying full-rank matrix (TVFRM) for engineering applications. Design/methodology/approach A fast-convergent zeroing neural network (FCZNN) is proposed, integrating a time-varying matrix-based error function (TVMBEF), a dynamic evolution law (DEL), a novel dynamic attenuation coefficient (NDAC) and a novel power-sigmoid smooth activation function (NPSSAF). Findings Theoretical analysis proves asymptotical and super-exponential convergence, and numerical simulations demonstrate superior performance in computing both right and left MPIs with minimal steady-state errors. The manipulator trajectory tracking experiment further confirms the superiority of FCZNN. Originality/value The study presents a novel FCZNN framework with adaptive NDAC and nonlinear NPSSAF, providing an effective solution for MPI of TVFRM and manipulator trajectory tracking control.