Distributed optimal sliding-mode consensus control for nonlinear vehicle platoon under intermittent denial-of-service attacks

This paper addresses the distributed resilient optimal sliding-mode consensus control of constrained vehicle platoons subject to intermittent denial-of-service (DoS) attacks and input delays. Radial-basis-function neural networks are adopted to approximate unknown system nonlinearities. First, a distributed switched observer is constructed to identify attack activation states, which enables attack-dependent switching logic under communication interruptions. Second, an adaptive sliding surface integrated with a tangent-type barrier Lyapunov function is designed to strictly enforce the vehicle platoon’s state safety constraints. This sliding surface is equipped with robust compensation and cooperative recovery components to sustain closed-loop stability during active DoS attacks. To balance tracking precision and control energy consumption, an actor-critic adaptive dynamic programming framework is embedded to online solve the optimal control problem. The cost function introduces an attack-aware penalty term to counteract performance losses induced by communication interruptions, while sliding-mode regulation provides inherent anti-disturbance robustness. Rigorous Lyapunov analysis proves all closed-loop signals are semi-globally uniformly ultimately bounded (SGUUB). The tracking errors converge to a small residual neighborhood of zero, and the proposed framework simultaneously satisfies predefined state constraints, mitigates intermittent DoS attacks, and compensates powertrain input delays. Numerical simulations on strict-feedback pendulum systems and a longitudinal vehicle platoon verify the theoretical validity and practical applicability of the developed control scheme.