H ∞ Optimal Tracking Control for Two-Time-Scale Supply Chain Systems Subject to DoS Attack

This article investigates the $H_{\infty }$ optimal tracking control problem for supply chain systems characterized by two distinct time scales and vulnerability to denial-of-service (DoS) attacks. To reduce the computational complexity and eliminate the sensitivity to time-scale variations inherent in traditional lifting techniques, the system is decomposed into fast and slow subsystems using singular perturbation theory. A policy iteration (PI)-based $H_{\infty }$ optimal control scheme is proposed to attenuate the bullwhip effect in supply chain systems, namely, the amplification of customer demand uncertainty throughout the network. The control scheme allows inventory levels to accurately track desired targets even in the presence of perturbations. To address the information loss caused by DoS attacks, a nonlinear autoregressive (NAR) neural network-based predictor is designed to provide real-time state compensation. The method's effectiveness is validated through a case study of a potassium carbonate production process. Simulation results demonstrate that the proposed approach reduces the bullwhip effect by 63% and provides superior steady-state accuracy and dynamic performance compared with the existing integral sliding-mode and standard policy-iteration methods.