Global sensitivity analysis for the boundary control of an open channel

TL;DR

This paper performs a global sensitivity analysis on the boundary control of an open water channel governed by Shallow Water equations, assessing how parameter uncertainties affect control outcomes.

Contribution

It introduces a method to analyze the impact of physical parameter uncertainties on boundary control of open channels using sensitivity indices.

Findings

First-order sensitivity indices quantify individual parameter impacts.

Total sensitivity indices reveal combined effects of parameters.

Numerical simulations demonstrate the approach's effectiveness.

Abstract

The goal of this paper is to solve the global sensitivity analysis for a particular control problem. More precisely, the boundary control problem of an open-water channel is considered, where the boundary conditions are defined by the position of a down stream overflow gate and an upper stream underflow gate. The dynamics of the water depth and of the water velocity are described by the Shallow Water equations, taking into account the bottom and friction slopes. Since some physical parameters are unknown, a stabilizing boundary control is first computed for their nominal values, and then a sensitivity anal-ysis is performed to measure the impact of the uncertainty in the parameters on a given to-be-controlled output. The unknown physical parameters are de-scribed by some probability distribution functions. Numerical simulations are performed to measure the first-order and total sensitivity indices.