Decentralized predictive control for 1D cascaded systems of conservation laws

In this work we investigate the predictive control problem for partial differential equations interconnected through their boundary conditions. More specifically, we consider systems of cascaded 1D hyperbolic equations. The main obstacle for applying model predictive control methodologies for such systems is the huge computational effort required to solve the corresponding optimization problems. Therefore, we present some results on decomposition methods. The obtained sub-problems are solved in parallel and considered as subsystems controlled by decentralized interacting agents. The proposed approach is validated in simulation for a free surface water transportation system made of interconnected canal reaches interconnected through actuated gates.