Adaptive state and parameter estimation for coupled ODE-wave PDE systems with uncertain dynamics

In this paper, we consider the problem of state and parameter estimation problem for an Ordinary differential equation-Partial differential equation (ODE-PDE) cascade system, in which the output of the ODE dynamics serves as the driving force for the PDE dynamics, governed by a wave equation. We develop an adaptive observer that combines a state observer with a least-squares parameter adaptation law and six auxiliary filters. A rigorous analysis of well-posedness and convergence properties is subsequently conducted. The estimated parameter value converged to the actual value exponentially under a specific persistent excitation condition. Numerical results demonstrate the effectiveness of the estimation scheme.