Finite-Time Reciprocal Zeroing Neural Network Model for Handling Temporal-Variant Linear Equations and Mobile Localization Problems

Temporal-variant linear equations (TVLEs) are widely acknowledged for their pivotal role in various engineering fields, offering a potent means to model dynamic processes and evolving relationships over time. A conventional approach involves leveraging the zeroing neural network (ZNN) model for tackling TVLE problems. In response to challenges associated with inverse matrix computations and infinite-time convergence constraints, we introduce an innovative single inverse-free finite-time reciprocal ZNN (FRZNN) model constructed to effectively address TVLE problems without using the activation functions. The convergence property and robustness of the FRZNN model are thoroughly examined adopting Lyapunov stability method of the nonlinear system and a comparative approach for nonlinear perturbed systems. Through two numerical experiments and an Angle-of-Arrival (AOA) simulation, the performance of the FRZNN model is thoroughly evaluated, revealing its validity and superior effectiveness when compared to state-of-the-art approaches. In detail, the performance improvement ratio (PIR) of the FRZNN model in addressing the AOA problem is 60.52%, and under a noise environment, the PIR of the FRZNN model is 99.99%.