Environmental management optimizing a long-run objective is an ergodic control problem whose resolution can be achieved by solving an associated non-local Hamilton-Jacobi-Bellman (HJB) equation having an effective Hamiltonian. Focusing on sediment storage management as a modern engineering problem, we formulate, analyze, and compute a new ergodic control problem under discrete observations: a simple but non-trivial mathematical problem. We give optimality and comparison results of the corresponding HJB equation having unique non-smoothness and discontinuity. To numerically compute HJB equations, we propose a new fast-sweep method resorting to neither pseudo-time integration nor vanishing discount. The optimal policy and the effective Hamiltonian are then computed simultaneously. Convergence rate of numerical solutions is computationally analyzed. An advanced robust control counterpart where the dynamics involve uncertainties is also numerically considered.

翻译：将沉积物储存管理作为现代工程问题的焦点,我们在离散观测中制定、分析并计算出一个新的垂直控制问题:一个简单但非三边数学问题。我们给出了具有独特非移动性和不连续性的相应的 HJB 等式的最佳性和比较结果。为了从数字上计算 HJB 等式,我们建议采用一种新的快速清除方法,既不使用假时间整合,也不使用消减法。然后同时计算最佳政策和有效的汉密尔顿式政策。对数字解决方案的趋同率进行了计算分析。在动态涉及不确定性的情况下,对先进的强力控制对等方也进行了数字上的考虑。