Differential dynamic programming for estuarine management

A differential dynamic programming (DDP) procedure is applied to solve both linear and nonlinear estuarine-management problems to determine the optimal amount of freshwater inflows into bays and estuaries to maximize fishery harvests. Fishery harvests are expressed in regression equations as functions of freshwater inflows. The optimization problem is posed as a discrete-time optimal control problem in which salinity represents the state variable and freshwater inflow represents the control variable. Both linear and nonlinear regression equations that relate salinity to freshwater inflow are used as the transition equations. The bound constraints for the control and state variables are incorporated into the objective function using a penalty-function method to convert the problem into an unconstrained formulation. To guarantee the quadratic convergence of the DDP procedure, a constant-shift and an adaptive-shift method are used. The DDP procedure is applied to the Lavaca-Tres Palacios estuary in Texas and the results are compared with a nonlinear programming solver. This work demonstrates the potential of DDP for developing a more complex model that uses a two-dimensional hydrodynamic-salinity transport model for the transition.