A new fixed-time stability of neural network to solve split convex feasibility problems

In this paper, we propose a novel neural network that achieves stability within the fixed time (NFxNN) based on projection to solve the split convex feasibility problems. Under the bounded linear regularity assumption, the NFxNN admits a solution of the split convex feasibility problem. We introduce the relationships between NFxNN and the corresponding neural networks. Additionally, we also prove the fixed-time stability of the NFxNN. The convergence time of the NFxNN is independent of the initial states. The effectiveness and superiority of the NFxNN are also demonstrated by numerical experiments compared with the other methods.