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We deal with a new maximum principle-based stochastic control model for rivermanagement through operating a dam and reservoir system. The model is based oncoupled forward-backward stochastic differential equations (FBSDEs) derivedfrom jump-driven streamflow dynamics and reservoir water balance. Acontinuous-time branching process with immigration driven by a tempered stablesubordinator efficiently describes clustered inflow streamflow dynamics. Thisis a completely new attempt in hydrology and control engineering. Applying astochastic maximum principle to the dynamics based on an objective functionalfor designing cost-efficient control of dam and reservoir systems leads to theFBSDEs as a system of optimality equations. The FBSDEs under a linear-quadraticansatz lead to a tractable model, while they are solved numerically in theother cases using a least-squares Monte-Carlo method. Optimal controls arefound in the former, while only sub-optimal ones are computable in the latterdue to a hard state constraint. Model parameters are successfully identifiedfrom a real data of a river in Japan having a dam and reservoir system. We alsoshow that the linear-quadratic case can capture the real operation data of thesystem with underestimation of the outflow discharge. More complex cases with arealistic time horizon are analyzed numerically to investigate impacts ofconsidering the environmental flows and seasonal operational purposes. Keychallenges towards more sophisticated modeling and analysis with jump-drivenFBSDEs are discussed as well.

Towards Control of Dam and Reservoir Systems with Forward-Backward Stochastic Differential Equations Driven by Clustered Jumps