Abstract
This paper studies the state estimation problem for a class of coupled linear ODE–hyperbolic PDE systems with unknown in-domain parameters. Based on the swapping transformation and the least squares parameter estimation method, a Luenberger-type adaptive boundary observer is designed to estimate the ODE–PDE states under the unknown parameters. The exponential convergence conditions w.r.t. the observer feedback gains are given by employing the Lyapunov technique. Finally, an application to traffic state estimation of the Aw–Rascle–Zhang (ARZ) model involving the unknown relaxation time and the boundary input speed deviation is provided to validate the theoretical result.
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