Boundary controllability of a system modelling a partially immersed obstacle

Gaston Vergara-Hermosilla, Günter Leugering, Yue Wang
2021 E S A I M: Control, Optimisation and Calculus of Variations  
In this paper, we address the problem of boundary controllability for the one-dimensional nonlinear shallow water system, describing the free surface flow of water as well as the flow under a fixed gate structure. The system of differential equations considered can be interpreted as a simplified model of a particular type of wave energy device converter called oscillating water column. The physical requirements naturally lead to the problem of exact controllability in a prescribed region. In
more » ... ticular, we use the concept of nodal profile controllability in which at a given point (the node) time-dependent profiles for the states are required to be reachable by boundary controls. By rewriting the system into a hyperbolic system with nonlocal boundary conditions, we at first establish the existence and uniqueness of the semi-global classical solution for the system, then get the local controllability and that of nodal profile using a constructive method. In addition, based on this constructive process, we provide an algorithmic concept to calculate the required boundary control function for generating a solution for solving this control problem.
doi:10.1051/cocv/2021076 fatcat:scdcvmsw2rfxxmzya23wivbslu