A parameter-changing zeroing neural network for solving linear equations with superior fixed-time convergence. (1st December 2022) - Xiao, Lin; He, Yongjun; Liao, Bolin
Abstract: Linear equations (LEs) play an essential role in mathematics. Nevertheless, the vast majority of fixed-parameter zeroing neural network (ZNN) models are not fast enough to solve LEs. So, a novel parameter-changing ZNN (PCZNN) is proposed and studied in the quest for resolving LEs more efficiently. In contrast to the conventional ZNN and finite-time ZNN (FTZNN), the tuning parameter of the presented PCZNN is time-varying, resulting in three advantages of the PCZNN model: (1) less time for parameter adjustment, (2) faster convergence rate, and (3) less conservative upper bound on the convergence time. Furthermore, the upper bound of convergence time is derived through analysis, which is independent of its initial value. Simulation comparisons conclude that the PCZNN model is more efficient than the ZNN and FTZNN models in solving LEs. Finally, the synchronization control experiments of chaotic systems by two ZNN models with time-varying parameters are offered to verify the superiority of the PCZNN model. Highlights: A parameter-changing zeroing neural network is proposed for solving linear equations. The less conservative upper bound of the convergence time is calculated. Illustrative examples reveal that the proposed model is the best one. Synchronization experiments of chaotic systems verify the superiority of the model.