An efficient implementation of Stochastic MPC for open channel water-level planning

Aspects of a Stochastic MPC approach to water-level planning for automated irrigation channels are studied in this paper. Given an uncertain schedule of flow demands and a model of the channel dynamics under low-level feedback control, the planning problem is to determine water-level references that lead to the satisfaction of chance-constraints on the transient response to changes in flow load, as demand varies across time in a way that it can deviate from the schedule. Stochastic MPC is a receding horizon, optimal control based approach to solving such problems. The chance-constrained optimisation problems involved are difficult to solve in general, and a scenario based approach is typically used to find approximate solutions. The main contribution of the paper is an efficient reformulation of the scenario optimisation problem by discarding redundant scenarios to further reduce the computational cost. The approach is applicable to linear systems with an uncertain additive input. The proposed strategy is applied to an automated irrigation channel in a simulation example.