Modeling and computation of cost-constrained adaptive environmental management with discrete observation and intervention

Abstract

Cost-constrained stochastic control problems that arise in environmental engineering are formulated based on ergodic control with seasonal dynamics, which are subject to time-discrete observation and intervention. In this study, a novel adaptive Erlangization is introduced as a flexible intervention scheme, in which the sum of the intervention and observation costs is constrained in the sense of an expectation. The Hamilton–Jacobi–Bellman (HJB) equation is formulated by utilizing the method of Lagrangian multipliers as an optimality equation that is subject to the constrained expectation. We demonstrate that the HJB equation has a closed-form solution for a specific sand replenishment problem. This solution is used as a benchmark to verify a numerical algorithm for computing the HJB equation. Computational examples that focus on a sand replenishment problem in a river reach of a dam and a management problem of aquatic vegetation in a shallow lake are presented.