Observer-Based Adaptive Control for a Coupled PDE-ODE System of a Flexible Wing

This article proposes an adaptive observer-based control to address the PDE-ODE coupled system of a flexible wing, where external disturbances and references have unknown frequencies, amplitudes, and phases. An exosystem is defined for the above signals, however with an unknown matrix and initial values. By finding its detectable form, an adaptive state-feedback control is designed based on an adaption law whose uncertainties are merely from the unknown exosystem matrix. In this case, filter systems are defined based on the tracking error and the observer of the PDE-ODE system, which further gives the equivalent state of the exosystem. By updating the adaption law based on the filter systems, an observer-based adaptive control is designed to guarantee the convergence of the tracking error of the closed-loop system. Two simulation results are provided and compared to demonstrate the robust output regulation of the closed-loop system.