Robust explicit model predictive control for uncertain multirate system

This paper studies robust explicit model predictive control for multirate system with bounded additive disturbances. First, based on dynamic programming, the optimization problem is decomposed into multi-stages of subproblems with one-step optimal horizon. In the process of solving the subproblem of each stage, considering the influence of additive disturbance, we construct the constraint set of the first predicted state, and then such a constraint set is transformed into the constraint condition dependent on current state and input. After that, the multiparametric quadratic programming (mp-QP) technique is used to obtain the robust explicit control laws. The robust positively invariant set of the multirate system is chosen as the terminal constraint set of the optimization problem such that the robust stability can be ensured. The numerical ex ample sho ws that the proposed robust explicit predictive control can reduce online computation and satisfy the demand of the multirate system with the fast update speed of input.