2020/01/04 by Hidekazu Yoshioka, Yoshioka, H., Yumi Yoshioka +1
Engineering · Environmental Science · #FOS: Electrical engineering #FOS: Mathematics #Flood Risk Assessment and Management #Hydrology and Watershed Management Studies #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Systems and Control (eess.SY) #Water resources management and optimization #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2001.02070
openalex publication_date 2020/01/04 · openalex created_date 2020/01/23 · openalex updated_date 2026/07/28
A new stochastic control problem of a dam-reservoir system installed in a river is analyzed both mathematically and numerically. Water balance dynamics of the reservoir are piece-wise deterministic and are driven by a stochastic regime-switching inflow process. The system is controlled to balance among the operation purpose and the internal and downstream environmental conditions. Finding the optimal operation policy of the system reduces to solving an optimality equation with a discontinuous Hamiltonian, which is a system of nonlinear degenerate parabolic (or hyperbolic) equations. We show that the optimality equation has at most one constrained viscosity solution and find the solution explicitly under certain conditions. The model is applied to numerical computation of the operation policy of an existing dam-reservoir system using a high-order finite difference scheme. The computational results can suggest how the operation policy should be adapted according to the environmental concerns of the river.