Intermittent Sampled-Data Control for Local Stabilization of Neural Networks Subject to Actuator Saturation: A Work-Interval-Dependent Functional Approach

• Published in: IEEE transaction on neural networks and learning systems Vol. 35; no. 1; pp. 1087 - 1097
• Main Authors: Ni, Yanyan, Wang, Zhen, Huang, Xia, Ma, Qian, Shen, Hao
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.01.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Actuator saturation; Actuators; Artificial neural networks; Closed loop systems; Closed loops; Control systems; Feedback control; intermittent sampled-data control (ISC); Linear matrix inequalities; local stabilization; Lyapunov functional; Neural networks; neural networks (NNs); Nonlinear systems; Stability criteria; Stabilization; Symmetric matrices; Synchronization
• ISSN: 2162-237X; 2162-2388; 2162-2388
• DOI: 10.1109/TNNLS.2022.3180076

This article is concerned with the local stabilization of neural networks (NNs) under intermittent sampled-data control (ISC) subject to actuator saturation. The issue is presented for two reasons: 1) the control input and the network bandwidth are always limited in practical engineering applications and 2) the existing analysis methods cannot handle the effect of the saturation nonlinearity and the ISC simultaneously. To overcome these difficulties, a work-interval-dependent Lyapunov functional is developed for the resulting closed-loop system, which is piecewise-defined, time-dependent, and also continuous. The main advantage of the proposed functional is that the information over the work interval is utilized. Based on the developed Lyapunov functional, the constraints on the basin of attraction (BoA) and the Lyapunov matrices are dropped. Then, using the generalized sector condition and the Lyapunov stability theory, two sufficient criteria for local exponential stability of the closed-loop system are developed. Moreover, two optimization strategies are put forward with the aim of enlarging the BoA and minimizing the actuator cost. Finally, two numerical examples are provided to exemplify the feasibility and reliability of the derived theoretical results.