Accelerated Finite-Time Inverse-Free ZND Model for Solving Dynamic Sylvester Matrix Equation Problems with Application

Dynamic Sylvester equations (DSEs) arise in a wide range of intelligent systems, including pole assignment for nonlinear time-varying systems, robotic motion generation, and adaptive control. Efficiently solving DSEs in real time is increasingly important for enabling responsive and reliable artificial intelligence applications. Existing approaches, including zeroing neural dynamics (ZND) and its variants, have achieved promising performance but still suffer from three limitations: dependence on matrix inversion with relatively high computational cost, asymptotic convergence behavior that limits response speed, and insufficient robustness under disturbances and numerical uncertainties. To address these limitations, this paper proposes an accelerated finite-time inverse-free zeroing neural dynamics (AFTIF-ZND) model for solving DSE problems. The proposed framework introduces an energy-cost scalar error formulation to eliminate explicit matrix inversion and establishes accelerated finite-time convergence with reduced computational complexity. Rigorous theoretical analyses are developed to characterize convergence, robustness, and disturbance tolerance. Numerical experiments together with path-tracking inverse-kinematics simulations and physical experiments on UR5, GEN3, and 10-DoF robotic platforms verify that the proposed method achieves superior computational efficiency, faster convergence, and improved robustness under dynamic conditions. The proposed framework advances real-time neural computation for dynamic matrix equations and provides a scalable mechanism for intelligent robotic control and adaptive AI-enabled decision systems.