Stochastic tubes in model predictive control with probabilistic constraints

Recent developments in stochastic MPC provided guarantees of closed loop stability and satisfaction of probabilistic and hard constraints. However the required computation can be formidable for anything other than short prediction horizons. This difficulty is removed in the current paper through the use of tubes of fixed cross-section and variable scaling. A model describing the evolution of predicted tube scalings simplifies the computation of stochastic tubes; furthermore this procedure can be performed offline. The resulting MPC scheme has a low online computational load even for long prediction horizons, thus allowing for performance improvements. The approach is illustrated by numerical examples.