Data-Driven Control for Local Stabilization of Neural Networks Subject to Input Saturation: A Memory-Type Event-Triggered Method

This article presents a data-driven control method to address the local asymptotic stabilization problem of discrete-time neural networks (DNNs) under input saturation. To reduce communication load, a memory-type event-triggered mechanism (MEM) is first designed to mitigate the superfluous triggers. Then, a memory-dependent Lyapunov function (MLF) is constructed to accommodate the memory term introduced by the MEM. Based on the designed MEM, the MLF and two data-based system representations, a data-based stabilization criterion is developed, and an estimated region of attraction (ERA) is determined. Simultaneously, the feedback gain and the trigger matrix are co-designed to guarantee the local stability of the closed-loop system. A notable feature of the proposed approach is that the proposed stabilization criteria rely solely on accessible data, without necessitating full knowledge of the system matrices. It makes the approach well-suited for practical applications where precise modeling is difficult or infeasible. Furthermore, a hybrid optimization scheme combining the linear objective minimization method and the particle swarm optimization (PSO) algorithm is presented to maximize the size of the ERA. Finally, two numerical simulations are given to validate the effectiveness of the proposed optimization algorithm, illustrate the influence of data size, and demonstrate the advantages of the designed MEM in stabilizing DNNs.