Observer of Coupled Hyperbolic PDEs for Deep-sea Construction Vessel Vibrations

Abstract Motivated by vibration state estimation of a deep-sea construction vessel used to install oil drilling equipment on the seafloor, this paper presents state observer design of a 4 × 4 coupled heterodirectional hyperbolic PDE-ODE system, characterized by spatially-varying coefficients and a time-varying domain. The exponential stability of the observer error system is proved via Lyapunov analysis. Effective estimation of lateral-longitudinal coupled vibration states of the deep-sea construction vessel is verified in numerical simulation.