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The goal of this paper is to solve the global sensitivity analysis for aparticular control problem. More precisely, the boundary control problem of anopen-water channel is considered, where the boundary conditions are defined bythe 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 theShallow Water equations, taking into account the bottom and friction slopes.Since some physical parameters are unknown, a stabilizing boundary control isfirst computed for their nominal values, and then a sensitivity anal-ysis isperformed to measure the impact of the uncertainty in the parameters on a givento-be-controlled output. The unknown physical parameters are de-scribed by someprobability distribution functions. Numerical simulations are performed tomeasure the first-order and total sensitivity indices.

Global sensitivity analysis for the boundary control of an open channel