Adaptive Neural Sliding Mode Control for Singularly Perturbed Systems With Randomly Perturbed Sampling Periods

This paper addresses the problem of adaptive neural network sliding mode control for sampled-data singularly perturbed systems subjected to randomly perturbed sampling periods and unrestricted deception attacks. In contrast to the conventional transition probabilities,the utilization of sojourn probabilities are essential to capture the inherent randomness associated with the sampling periods. Furthermore, in the presence of unrestricted deception attacks, a neural network-based approach is utilized to estimate and mitigate their impact on system performance. Additionally, a sliding mode controller is developed based on both the sampling period mode and the singularly perturbed parameter. This controller ensures the exponential ultimate boundedness in the mean square sense and the reachability of the specified sliding surface for the closed-loop system. Finally, the proposed theory is validated through a practical example, demonstrating its effectiveness and soundness. Note to Practitioners — Due to the advent of the digital era, periodically sampled-data systems have received much attention. However, practical engineering conditions often introduce non-ideal factors, such as network congestion, noise interference, and voltage instability, which can cause randomly perturbed sampling. As considered in this paper, a sojourn probability, which is more easily obtained by statistical methods, is applied to model the variation of sampling periods. On the other hand, in real network environments, the boundedness of an attacker’s injection attack cannot be guaranteed. Therefore, in this paper, we consider using a neural network-based approach to estimate and mitigate their impact on system performance in the presence of unrestricted deception attacks. Meanwhile, sliding mode control, which has drawn widespread attention for its cost-saving and reliability, is utilized to achieve exponential ultimate boundedness in the mean square sense and reachability of the specified sliding surface of the controlled system.