Scenario and Adaptive Model Predictive Control of Uncertain Systems

Two recent predictive control approaches for constrained systems subject to uncertainty are reviewed. The first one, named scenario MPC, is best suited for stochastic systems where a certain share of constraint violations is tolerated and rewarded. The approach is able to control precisely the share of violations that occur during closed loop operation, under quite general assumptions on the involved stochastic variables. The second technique, named adaptive MPC, is cast in a different framework, where the aim is to enforce robustly the system cnstraints and a stochastic characterization of the uncertainty is not required. The algorithm embeds a real-time set membership identification strategy that yields a refined set of unfalsified models at each time step, hence reducing the size of the model uncertainty and improving the closed loop performance over time. After recalling the main results pertaining to each approach, their applicability, strengths and weaknesses are discussed, as well as open issues that can be subject of future research.