Prescribed-Time Delayed Zeroing Neural Network for Solving Time-Varying Equations and Its Applications

Zeroing neural networks (ZNNs) play a crucial role in efficiently solving time-varying problems. Recently, ZNNs are integrated with many advanced control theories with a certain convergence time to enhance their performance. On account of the convergence time of the prescribed-time convergence is precise, it is of great significance to investigate ZNN with prescribed-time convergence. In addition, delay is unavoidable in circuit implementation, not only impacting the prescribed-time convergence but also inducing instability and oscillation in ZNN. To evaluate the effectiveness of prescribed-time ZNN under delay environment, prescribed-time delayed zeroing neural network (PTDZNN) is proposed for solving time-varying equations in this article. It is concluded that PTDZNN can obtain the correct real-time solution in prescribed time and the convergence time of PTDZNN is independent of initial conditions. Furthermore, PTDZNN exhibits notable tolerance to delay and distinguishes itself from existing delayed zeroing neural networks by its independence from linear matrix inequality (LMI). Moreover, the LMI-independent stability proof of ZNN under delay environment is also proved. Numerical simulations are presented to demonstrate the prescribed-time convergence and delay tolerance of PTDZNN. Ultimately, PTDZNN is successfully applied in dynamic positioning algorithms and image fusion problems. Notably, PTDZNN stands out as the first ZNN to incorporate both prescribed-time convergence and delay.