Reciprocal-Type Zeroing Neural Dynamics Model for Tackling Time-Dependent Lyapunov Matrix Equation Problems and Applications
提出一种免矩阵求逆的互易型归零神经动力学模型，用于高效求解时变李雅普诺夫矩阵方程，并通过线性与非线性系统案例验证其实用价值。
Time-dependent Lyapunov matrix equation (TDLME) plays a central role in the control of linear and nonlinear systems. Existing models, including the classical zeroing neural dynamics (ZNDs) model and its variants, have been used to address the TDLME problem. However, those models require time-dependent matrix inversion, which is computationally demanding, and they primarily focus on measurement-related noise, overlooking other sources of system uncertainty. To overcome these challenges, we propose an inverse-free reciprocal-type ZND (RTZND) model. This model integrates an energy-based error function with the ZND framework, eliminating the need for matrix inversion and incorporating error-feedback-related noise through its closed-loop control structure. We establish the convergence and robustness of the RTZND model using Lyapunov stability theory and assess its performance under external disturbances. Numerical simulations confirm its effectiveness and improved computational efficiency in solving the TDLME problem. We further confirm its applicability through two case studies, a time-dependent linear system and a nonlinear system modeled by the single machine infinite bus (SMIB) system, highlighting the RTZND model’s practical value in addressing TDLME problems.