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Global sensitivity analysis for the boundary control of an open channel

  • Alexandre Janon
  • Maëlle Nodet
  • Christophe Prieur
  • Clémentine Prieur
Original Article

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 analysis is performed to measure the impact of the uncertainty in the parameters on a given to-be-controlled output. The unknown physical parameters are described by some probability distribution functions. Numerical simulations are performed to measure the first-order and total sensitivity indices.

Keywords

Sensitivity analysis Shallow-Water equation Saint Venant equation Control Sobol indices Metamodel 

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Copyright information

© Springer-Verlag London 2015

Authors and Affiliations

  • Alexandre Janon
    • 1
  • Maëlle Nodet
    • 2
  • Christophe Prieur
    • 3
  • Clémentine Prieur
    • 2
  1. 1.Laboratoire de Mathématiques d’OrsayUniversité Paris-Sud, CNRSOrsayFrance
  2. 2.Université Grenoble Alpes, CNRS, INRIAGrenobleFrance
  3. 3.Gipsa-lab, CNRSGrenobleFrance

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