Stabilization of a Solitary Wave in a Spatio Temporal 1D Uncertain Navier-Stokes Equation by Passivity Based Boundary Control

In this paper is presented a stabilization technique for a solitary wave found in a spatio-temporal 1D uncertain Navier-Stokes equation by passivity based control. First, a full dynamic analysis is proposed in order to take into consideration the characteristics of the solitary wave found in this Navier-Stokes equation. This analysis consists into the separation of the solitary wave found in the Navier-Stokes equation. This research study aims to stabilizes the solitary waves found in a numerical wave tank water reservoir. By this way the main objective is to protect renewable energy systems, such as offshore aeolic or wave energy converter renewable energy systems. The passivity based boundary controller designed in this research study consists into the selection of an appropriate Lyapunov functional to select the appropriate boundary control law. It is important to recall also, that the input-output characteristics of the 1D uncertain Navier-Stokes equation allows us to establish the appropriate storage function in order to focus in the stabilization of the solitary wave found in this mathematical model. Extensive simulations are performed in order to validate the theoretical results found in this research study. The discussions and conclusions of this work are presented.