Optimal control of waves generators in a canal
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The paper is devoted to the control of the movement of water in a canal. Waves are created by one (or two) plane generators located at one (or two) end(s) of the canal. The objective is to obtain a given wave by acting on the velocities of generators considered as control functions. The model of such a system is given by a classical linear model of shallow water, which leads to an "hyperbolic" equation. The method proposed here to solve the optimal control problem combines the use of a spectral basis to approximate the state and a Fourier series to represent the control. The final problem reduces to a linear system, the solution of which being very fast. The numerical experiments show that it is possible to create a progressive wave in a short canal during quite long time by mean of two generators, whereas classical canals with only one generator are significantly longer.
KeywordsOptimal Control Problem Plane Generator Fundamental Period Exact Controllability Progressive Wave
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