Adaptive observer design for wave PDEs with nonlinear dynamics and parameter uncertainty. (January 2021) - Benabdelhadi, Abdeljalil
Abstract: We consider the problem of state observer design for wave PDEs containing Lipschitz nonlinearities in the domain and parameter uncertainties in the domain and at the boundaries. Using the decoupling-transformation design approach, we develop an adaptive boundary observer consisting of a state observer, a least-squares type parameter adaptive law, and a hyperbolic auxiliary filter. Using Lyapunov stability analysis, we show that the observer is exponentially convergent under a persistent excitation condition. The novelty is twofold: (i) the class of systems is much wider than those studied in previous works, it particularly accounts for structured disturbances acting on the domain and all boundaries; (ii) the proposed adaptive observer is quite different from existing ones for wave-type PDEs.