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This article presents a robust model predictive control (MPC) for piecewise constant reference tracking based on a constrained linear model and a terminal constraint defined from the admissible equilibria set. The new robust MPC algorithm based on nominal predictions ensures recursive feasibility and convergence to an optimal target, but the terminal constraint is derived from an admissible equilibria set with a suitable disturbance translation. The computation of the proposed terminal constraint is simple because no subset verification is required and the number of half-spaces of the proposed terminal constraint is fixed a priori. A zonotope disturbance bound description is used to simplify the computation of the admissible equilibria. Furthermore, it is shown that the proposed strategy can be directly extended to other MPC algorithms based on artificial targets, as a stochastic MPC based on the individual chance constraints, for instance. Two case studies are used to illustrate the usefulness of the proposed robust MPC for piecewise constant set-point tracking based on nominal predictions.

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