Numerical solution of optimal control problems for the Shallow water equation

The shallow water equations are hyperbolic partial differential equations (or parabolic if viscous shear is considered) that describe the flow below a pressure surface in a fluid. They are modeling fluid dynamics phenomena where the horizontal length scale is much greater than the vertical length scale, e.g., in the atmosphere and the oceans. Moreover, models of water reservoirs, lakes and rivers have been proposed in the literature; in particular methods to control the flow behavior to prevent the effects of floods.

In this project, we investigate the numerical solution of the optimal control problems for the shallow water equation in concrete applications. Instead of viewing this problem as an unconstrained optimization problem after discretization of the corresponding optimality system, we solve the closed loop problem. Solving this type of control problem has many advantages compare to an open-loop approach from engineering point of view. For these type of control problems two different optimization goals can be analyzed: one can be seen as stabilization of the plant model, the second one is of tracking type, i.e., a given (optimal) solution trajectory is to be attained. Moreover, we are going to investigate the application of the linear quadratic Gaussian desing, which is a combination of the linear quadratic estimator and the LQR problem.

Tags: Optimal control