Environmental management should be based on a long-run sustainable viewpoint. A stochastic control problem optimizing a long-run objective function is an ergodic control problem whose resolution can be achieved by solving an associated  Hamilton-Jacobi-Bellman (HJB) equation having an effective Hamiltonian. However, this key topic has not been well-studied in the context of environmental management. Focusing on non-smooth sediment storage management as an engineering problem, we formulate  a new ergodic control problem under discrete observations: a natural assumption of realistic observations . We give an analytical solution to a simple problem and verify optimality and uniqueness of the corresponding HJB equation . To manage HJB equationsin more general cases , we propose a fast sweep method resorting to neither pseudo-time integration nor vanishing discount. The optimal policy and the effective Hamiltonian are then computed simultaneously. A robust control counterpart where the dynamics involve uncertainties is also considered based on a multiplier robust formalism that harmonizes with the stochastic control approach. The resulting HJB equation has a stronger non-linearity but is managed using the presented numerical method. An extended problem constraining control policy is analyzed as well .
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 .
D
should be based on a long-run sustainable viewpoint. A stochastic control problem
D
function
A
non-local
R
However, this key topic has not been well-studied in the context of environmental management. Focusing on non-smooth
Focusing on
R
an
a modern
A
, analyze, and compute
R
natural assumption of realistic observations
simple but non-trivial mathematical problem
R
an analytical solution to a simple problem and verify optimality and uniqueness
optimality and comparison results
R
. To manage HJB equationsin more general cases
having unique non-smoothness and discontinuity. To numerically compute HJB equations
R
fast sweep
new fast-sweep
R
A
Convergence rate of numerical solutions is computationally analyzed. An advanced
R
considered based on a multiplier robust formalism that harmonizes with the stochastic control approach. The resulting HJB equation has a stronger non-linearity but is managed using the presented numerical method. An extended problem constraining control policy is analyzed as well
numerically considered