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.

对安装在河流中的大坝－水库系统的一个新的随机控制问题进行了数学和数值分析。水库的水平衡动力学是分段确定性的，并由随机状态切换流入过程驱动。控制该系统以在操作目的与内部和下游环境条件之间取得平衡。寻找系统的最佳操作策略可以简化为用不连续哈密顿量求解最优方程，该哈密顿方程是非线性简并抛物线（或双曲）方程组。我们表明，最优方程最多具有一个约束粘度解，并且在某些条件下可以明确找到该解。该模型适用于使用高阶有限差分方案的现有大坝—水库系统运行策略的数值计算。计算结果可以建议应如何根据河流的环境问题来调整运营策略。