Model Predictive Control With Mixed Performances for Uncertain Positive Systems

This paper addresses the model predictive control for positive systems with uncertainty and exogenous disturbance input. By utilizing a linear Lyapunov function, a sequence of model predictive controllers for positive systems is designed based on multi-step control sets guaranteeing robust stability with mixed performances. A sequence of cone sets is chosen as the invariant sets of the model predictive control. With the above idea, a model predictive control algorithm is established to compute the optimal value of the mixed performances. All conditions are in terms of linear programming to cope with largescale computation with low computation burden. Finally, a numerical example is provided to verify the effectiveness of the proposed design.