Regime-switching constrained viscosity solutions approach for controlling dam-reservoir systems
Regime-switching constrained viscosity solutions approach for controlling dam-reservoir systems
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DOI：
10.1016/j.camwa.2020.09.005
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发表时间：
2020-01
期刊：
影响因子：
--
通讯作者：
H. Yoshioka;Y. Yoshioka
中科院分区：
文献类型：
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作者：
H. Yoshioka;Y. Yoshioka
对河流中坝库系统的一个新的随机控制问题进行了数学和数值分析。水库的水平衡动态是分段确定性的，并由随机状态切换流入过程驱动。控制系统以平衡操作目的和内部及下游环境条件。寻找系统的最优运行策略归结为求解一个具有不连续哈密顿量的最优性方程，这是一个非线性退化抛物（或双曲）方程组。我们证明了最优性方程最多有一个约束粘性解，并在一定条件下找到了解。该模型应用于数值计算的一个现有的坝库系统的运行策略，使用高阶有限差分格式。计算结果可为河流环境问题的处理提供参考。
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.