Assessment and Future Directions of Nonlinear Model Predictive ...

266 M. Cannon, P. Couchmann, and B. KouvaritakisFig. 2. Stochastic MPC closed-loop responses for p 2 = 0.85 and 20 uncertaintyrealizations (dark lines show responses for a single uncertainty realization)Fig. 3. Robust MPC closed-loop responses for 85% confidence levels and the same setof uncertainty realizations as in Fig. 2uncertainty realizations. The higher degree of conservativeness and greater variabilityin Fig. 3 is a result of the robust min-max strategy, which attempts tocontrol worst-case predictions based on the confidence bounds of (27), whereasthe stochastic MPC strategy (Fig. 2) has direct control over the statistics offuture predictions at each sampling instant.Consider next the effects of approximating uncertainty in the input map asoutput map uncertainty. Modelling uncertainty in plant parameters as outputmap uncertainty simplifies MPC design since state predictions are then deterministic,but can result in a higher degree of suboptimality. Thus for the 3rdorder plant model: