Suboptimal Hybrid Model Predictive Control: Application to Sewer Networks

This paper presents an application of the suboptimal hybrid model predictive control (HMPC) algorithm previously proposed by the authors to large scale sewer networks. HMPC relies on the on-line solution of mixed integer programs (MIP) that are known to be NP-complete and whose worst case complexity scales exponentially with problem size. Modern MIP solvers are on the other hand highly efficient at taking advantage of problem structure and usually achieve average optimization times that are much better than the worst case predicts. But as the MIP constraints depend on the current state of the plant, complexity can vary considerably and unpredictable behavior can occur. To circumvent unpredictability and to be able to enforce hard real-time computation constraints, the number of feasible nodes in the MIP problem is limited online by adding constraints to the number of possible mode sequences over the prediction horizon. It is shown that in realistic scenarios concerning control of large scale sewer networks, depending on the value of parameters related to the mode sequence constraints (MSC), drastic reductions can be achieved in optimization time. Practical issues of the approach are also addressed.