Estuary management by stochastic linear quadratic optimal control

A new type of estuary-management model based on discrete-time stochastic linear quadratic optimal control is presented. It is a feedback-control model that enables decision makers to determine the upstream reservoir releases during a time interval after the salinity and nutrient levels are observed at specified locations in the estuary at the beginning of the time interval. The optimal upstream reservoir releases are determined so that the salinity and nutrient levels at these locations are as close as possible to the prescribed levels for the remaining time intervals in the sense of statistical expectation. The ungauged inflows, precipitation, and evaporation are incorporated into the model as random variables. The control vector for the estuarine system consists of the freshwater inflows into the estuary, and the state vector contains the salinity and nutrient levels at specified locations for measurement in the estuary. The dynamic-programming principle is used to analytically derive the feedback-control law that expresses the control vector as a linear function of the state vector. The parameter matrix in the system equation is recursively updated by recursive least squares. Numerical examples are performed for the Lavaca-Tres Palacios Estuary in Texas for the purposes of illustrating the viability of this methodology.