Model predictive control for a class of systems with uncertainty in scheduled load

This paper considers the problem of following open-loop trajectories that are in some sense optimal for a nominal load schedule. A Model Predictive Control (MPC) scheme is formulated to adjust the nominal open-loop control based on measurements taken at each time-step, with a view to mitigating uncertainty in the schedule. Analysis results are derived to establish recursive feasibility of the receding horizon scheme and to prove closed-loop stability for an appropriate set of initial conditions. An equivalent affine disturbance feedback parametrisation of the adjustment policy is provided for efficient computation. Simulation results for a short stretch of an irrigation channel demonstrate the effectiveness of the scheme.