Modeling stochastic operation of reservoir under ambiguity with an emphasis on river management.

Yoshioka, Hidekazu; Yoshioka, Yumi

Summary: An optimization problem of controlling a dam installed in a river is analyzed based on a stochastic control formalism of a diffusion process under model ambiguity: a new mathematical approach to this issue. The diffusion process is a pathwise unique solution to a water balance equation considering the inflow, outflow, water loss in the reservoir, and direct rainfall. Finding the optimal reservoir operation policy reduces to solving a degenerate parabolic partial differential equation: a Hamilton‐Jacobi‐Bellman‐Isaacs equation. A monotone finite difference scheme is constructed for discretization of the equation, successfully generating nonoscillatory and reasonably accurate numerical solutions. Stability analysis of the resulting water balance dynamics is finally carried out for both environmentally friendly and not friendly reservoir operations.

PARABOLIC differential equations; STOCHASTIC models; RESERVOIRS; FINITE differences; DIFFUSION processes; AMBIGUITY

Optimal Control - Applications & Methods, 2019, Vol 40, Issue 4, p764

0143-2087

Academic Journal

10.1002/oca.2510