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Global sensitivity analysis for the boundary control of an open channel. (English) Zbl 1338.93128

Summary: 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.

MSC:

93B35 Sensitivity (robustness)
93C20 Control/observation systems governed by partial differential equations
93C10 Nonlinear systems in control theory
35Q35 PDEs in connection with fluid mechanics

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References:

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