论文标题
在环境管理中引起的千古控制问题的分析和数值解决方案
Analytical and numerical solutions to ergodic control problems arising in environmental management
论文作者
论文摘要
环境管理优化长期目标是一个崇高的控制问题，可以通过解决具有有效汉密尔顿的相关的非本地汉密尔顿 - 雅各比 - 贝尔曼（HJB）方程来实现其解决方案。在离散观察结果下，我们将重点放在沉积物存储管理作为现代工程问题的情况下，制定，分析和计算一个新的Ergodic控制问题：一个简单但非平凡的数学问题。我们给出具有独特的非平滑度和不连续性的相应HJB方程的最佳和比较结果。要计算HJB方程式，我们提出了一种新的快速扫描方法，该方法既不是伪时间集成也不消失的折扣。然后同时计算最佳政策和有效的哈密顿量。数值解的收敛速率是计算分析的。还考虑了一个高级鲁棒控制对应物，其中还考虑了涉及不确定性的动力学。
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.
