论文标题
控制大坝 - 库库系统的政权开关粘度解决方案方法
Regime-switching constrained viscosity solutions approach for controlling dam-reservoir systems
论文作者
论文摘要
在数学和数值上分析了在河流中安装的大坝 - 水库系统的新的随机控制问题。储层的水平衡动力学是零件的确定性，并由随机切换的流入过程驱动。该系统受到控制，以在操作目的以及内部和下游环境条件之间平衡。找到系统的最佳操作策略可以减少使用不连续的哈密顿式求解最优方程，该方程是非线性退化抛物线（或双曲线）方程的系统。我们表明，最佳方程最多具有一个约束的粘度解决方案，并在某些条件下明确找到解决方案。该模型应用于使用高阶差异方案的现有大坝库系统操作策略的数值计算。计算结果可以表明如何根据河流的环境问题对操作策略进行调整。
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.
