Differential dynamic programming for estuarine management

Differential dynamic programming (DDP) is applied to solve the estuarine management problem to determine the optimal amount of freshwater inflows into bays and estuaries in order to maximize fishery harvests. 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. The hydrodynamic-salinity transport model HYD-SAL is used as the transition equation. The bound constraints for the control and state variables are incorporated into the objective function using the penalty function method to convert the problem into an unconstrained problem. The Successive Approximation Linear Quadratic Regulator (SALQR) is adopted to solve the computational complexity of the derivatives of the transition equation. The adaptive shift procedure is used to guarantee quadratic convergence of the DDP procedure. To consider the sensitivity of initial solutions, the step search technique of the unconstrained DDP is modified. Computational results indicate that the modified DDP method converges fast and initial values attempted converged to a unique optimal solution. The modified DDP procedure is applied to the Lavaca-Tres Palacios estuary in Texas.