An Infinite-Dimensional Luenberger-Like Observer for Water Waves

The paper deals with the observation problem by using an infinite dimensional observer for the water wave system governed by linearized water wave partial differential equations. We consider that the water wave system evolves in some infinite-dimensional Hilbert space. The output measurement of dynamical system is supposed to be the water wave surface elevation. An infinite-dimensional exponentially convergent Luenberger-like observer is proposed to estimate the states of water water system: water velocity potential and surface elevation. Numerical simulations by the finite difference scheme are carried out to validate the proposed observer.