RBF neural network-based adaptive control for Aw–Rascle–Zhang mixed traffic flow model with unknown external disturbances

This paper presents an adaptive control strategy for stabilizing mixed traffic flow dynamics governed by the Aw–Rascle–Zhang (ARZ) model under unknown spatiotemporal disturbances. To address the limitations of passive robustness in conventional approaches, a radial basis function neural network (RBFNN)-based disturbance observer is proposed for the active estimation and compensation of unknown spatiotemporal disturbances. Initially, a linearized hyperbolic partial differential equation (PDE) model is derived by employing the classical ARZ framework to characterize macroscopic mixed traffic behavior in congested segments containing both manually driven and adaptive cruise control (ACC)-equipped vehicles. Subsequently, an adaptive controller is proposed, which incorporates a disturbance observer based on an RBFNN, to stabilize the errors in both traffic density and velocity states. Then, a sufficient condition is established through an enhanced Lyapunov direct method to guarantee the exponential convergence of spatiotemporal states, even in the presence of unknown external disturbances. Finally, extensive comparative numerical simulations have been conducted under various ACC penetration rates, different external disturbances, diverse control strategies, and distinct observers. The effectiveness and superiority of the proposed RBFNN-based disturbance observer controller are demonstrated through quantitative evaluations of performance metrics, including disturbance estimation accuracy, fuel consumption, and driving comfort. To sum up, this paper not only establishes a theoretical foundation for controlling ACC-equipped vehicles in disturbed mixed traffic flow systems, but also facilitates the extension of the hyperbolic PDEs-based controller design methodology to practical real-world transportation applications.