Stochastic intervention strategy applied to a level control with a trade-off between risky operation and actuator variations

An approach for fluid level control is proposed here for a tank system subject to uncertain liquid inflow. The problem is motivated by an undersea tank gas/liquid separator that is being introduced in deepwater oilfields. There is no strict control regulator problem, but acting freely and continuously in the controlled pump may drastically shorten the lifetime of the equipment. To prevent premature worn with halt in the oil production, the control input variations should be meager and activated only with a view on risky operation. This control problem is coined here in the context of stochastic impulse control, which can be transformed in a sequence of iterated optimal stopping problems and expressed equivalently as a sequence of variational inequalities. A numerical solution is proposed, based on the Mean Value Scheme (MVS) method.