Computational Optimal Boundary Control for Water Pressure Suppression Arising in a Fluid Flow System Modeled by Hyperbolic PDEs

In this paper, we propose an efficient computational boundary control strategy for reducing water pressure shock effects generated by the suddenly operation of the valve closure located at the end of a fluid flow pipeline. First, we model the dynamic of the fluid flow transmission system as a coupled hyperbolic partial differential equations (PDEs), and then the water pressure suppression problem is formulated as a finite-time PDE-constrained optimal control problem. Second, we directly parameterize the time-varying boundary control input as a set of basic piecewise-quadratic functions which are needed to be optimized, the penalty function method is also introduced to deal with the inequality control constraint. As a result, the original PDE-constrained problem is transformed as a sequence of parameter optimization problems which can be easily solved by using existing gradient-based methods such as sequential quadratic programming (SQP). The exact gradient formulas of the cost function are derived analytically by using adjoint-based sensitivity analysis method. Finally, numerical simulations are illustrated to demonstrate our designed computational optimal boundary controller can significantly reduce the water pressure shock and fluctuation in the fluid flow transmission system.