Predictive Control With Guaranteed Stability for Water Hammer Equations
Résumé
We study the application of the receding horizon optimal control (RHOC) for hydraulic pipeline systems described by the so-called water hammer equations. Sufficient conditions to guarantee an asymptotic stability to an equilibrium state are first introduced and then integrated in the RHOC scheme. For the implementation, calculus of variations is employed to characterize the optimal solution in terms of the adjoint state and the recently proposed Lattice Boltzmann method is used to solve both direct and adjoint partial differential equations. This approach is finally validated in simulation.