Observer-Based Adaptive Estimation for Time Delay Hyperbolic PDE Systems With Application to Traffic Dynamics

Abstract

This paper presents the design of a Luenberger-type adaptive boundary observer for a class of linear hyperbolic partial differential equation models describing traffic dynamics. The observer enables online joint estimation of the traffic flow system state and unknown parameter using boundary measurement data. By integrating swapping transformations with adaptive parameter update law, the observer effectively reconstructs the traffic state and identifies parameter, mitigating traffic oscillations and congestion propagation. A Lyapunov-based stability analysis demonstrates that the estimation errors for both the state and parameters converge exponentially to a bounded residual set, provided the observer gain satisfies a specific linear matrix inequality. The effectiveness of the proposed design is validated using real-world traffic data from the NGSIM US 101 dataset.