Stochastic optimal control and parameter estimation for an estuary system

The study discussed two major parts which were stochastic optimal control and parameter estimation for an estuary system. The dissertation was divided into three phases. Phase 1 gave the background information on the classical optimal control theory and applied the Hamilton-Jacobi-Bellman's differential equation, Pontryagin's minimum principle, and the Euler-Lagrange differential equation to reservoir and river management. Phase 2 discussed a real-time lumped-parameter estuary system management model based upon stochastic linear quadratic feedback optimal control and recursive parameter estimation. Phase 3 discussed a real-time distributed-parameter estuary system management model based upon stochastic linear quadratic feedback optimal control and parameter estimation with uncertainty analysis. The estuary management models in Phase 2 and Phase 3 were applied to the Lavaca-Tres Palacios Estuary in Texas.;The feedback control methods provide a feedback mechanism of observed state variables (salinity or other nutrient) to the determination of the real-time control process. It can be used to implicitly reduce various kinds of uncertainties acting on the estuary system. Using the control law, decision makers can determine the optimal freshwater inflows during a month after the salinity and/or other nutrient values have been observed at the beginning of that month. The numerical results show that the optimal monthly inflows from the Lavaca-Navidad River and the Colorado River reasonably respond to different kinds of patterns of the observed salinity values.;The control problem for both the lumped-parameter and distributed-parameter estuary systems was to determine the optimal freshwater inflows into the estuary such that the desirable environmental conditions were reached. The lumped-parameter estuary system considered in this study was related to ARMAX (AutoRegressive, Moving Average, with eXogenous input) model while the distributed-parameter estuary system was the two-dimensional hydrodynamic and salinity transport partial differential equations. The parameter estimation technique for the lumped-parameter system was the recursive least squares. The parameter estimation technique for the distributed parameter system was based on the Gauss-Newton minimization technique in conjunction with the uncertainty analysis methods such as F.O.S.M., Rosenblueth's point-estimate, and Harr's point-estimate. The stochastic real-time optimal control for both lumped and distributed parameter systems was based upon stochastic linear quadratic feedback optimal control. The optimal control law was analytically derived by using dynamic programming's principle of optimality. The distributed-parameter system for control was related to a perturbation model for the two-dimensional HYD-SAL model.