Local minima of quadratic functionals and control of hydro-electric power stations. (English) Zbl 1331.49046
Summary: We consider a control problem for a cascade of hydro-electric power stations, where some of the stations have reversible turbines. Our aim was to optimize the profit of power production satisfying restrictions on the water level in the reservoirs. From the mathematical point of view, this consists in minimizing an infinite-dimensional quadratic functional subject to cone constraints. Sufficient conditions of optimality for the abstract problem are derived and are then specialized for our problem. Noteworthy, the restrictions imposed on the power stations problem are in the form of control constraints and pure state constraints. The particular case of one power station is analyzed in detail, showing that reversible turbines always improve the profit.
MSC:
49N10 | Linear-quadratic optimal control problems |
49N15 | Duality theory (optimization) |
49K15 | Optimality conditions for problems involving ordinary differential equations |
49K27 | Optimality conditions for problems in abstract spaces |
49N90 | Applications of optimal control and differential games |
Keywords:
optimal control; pure state constraints; quadratic functionals; maximum principle; hydro-electric power stationsReferences:
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