Fishways Design: An Application of the Optimal Control Theory

L. J. Alvarez-Vázquez (), A. Martínez (), M. E. Vázquez-Méndez () and M. A. Vilar ()
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L. J. Alvarez-Vázquez: Universidad de Vigo, Departamento de Matemática Aplicada II. ETSI Telecomunicación
A. Martínez: Universidad de Vigo, Departamento de Matemática Aplicada II. ETSI Telecomunicación
M. E. Vázquez-Méndez: Universidad de Santiago de Compostela, Departamento de Matemática Aplicada. Escola Politécnica Superior
M. A. Vilar: Universidad de Santiago de Compostela, Departamento de Matemática Aplicada. Escola Politécnica Superior

A chapter in Numerical Mathematics and Advanced Applications, 2008, pp 581-588 from Springer

Abstract: Abstract The main objective of this work is to present an application of mathematical modelling and optimal control theory to an ecological engineering problem related to preserve and enhance natural stocks of salmon and other fish which migrate between saltwater to freshwater. Particularly, we study the design (first) and the management (second) of a hydraulic structure (fishway) that enable fish to overcome stream obstructions as a dam or a weir. The problems are formulated within the framework of the optimal control of partial differential equations. They are approximated by discrete unconstrained optimization problems and then, solved by using a gradient free method (the Nelder-Mead algorithm). Finally, numerical results are showed for a standard real-world situation.

Keywords: Water Velocity; Shallow Water Equation; Hydraulic Structure; Optimal Control Theory; Target Velocity (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/978-3-540-69777-0_69

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