Recent developments in the numerical simulation of shallow water equations I: boundary conditions
Selected papers of the IMACS conference on Innovative methods in numerical analysis
Application of optimal control theory to bioremediation
Journal of Computational and Applied Mathematics - control of partial differential equations
Theoretical and Numerical Analysis of an Optimal Control Problem Related to Wastewater Treatment
SIAM Journal on Control and Optimization
Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions
SIAM Journal on Optimization
SIAM Journal on Optimization
Numerical Optimization for the Location of Wastewater Outfalls
Computational Optimization and Applications
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Fishways are the main type of hydraulic devices currently used to facilitate migration of fish past obstructions (dams, waterfalls, rapids,...) in rivers. In this paper we present a mathematical formulation of an optimal control problem related to the optimal management of a vertical slot fishway, where the state system is given by the shallow water equations, the control is the flux of inflow water, and the cost function reflects the need of rest areas for fish and of a water velocity suitable for fish leaping and swimming capabilities. We give a first-order optimality condition for characterizing the optimal solutions of this problem. From a numerical point of view, we use a characteristic-Galerkin method for solving the shallow water equations, and we use an optimization algorithm for the computation of the optimal control. Finally, we present numerical results obtained for the realistic case of a standard nine pools fishway.