Tractable robust MPC for tracking piecewise constant references based on nominal predictions

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This paper proposes two tractable linear MPC strategies for robust piecewise constant reference tracking in the presence of bounded disturbances. The definition of the stabilizing ingredients are simplified so that the offline computational burden of the robust MPC for tracking becomes similar to the non-robust MPC version. An implicit characterization of the Maximal Robust Positively Invariant (MRPI) set for tracking is used in the first robust MPC algorithm. Alternatively, a terminal equilibrium constraint with a slack variable is proposed to provide a further terminal set simplification in the second MPC approach. It is shown that recursive feasibility and Input-to-State Stability are preserved despite the proposed simplifications. A numerical case study that simulates a multivariable chemical process and a double integrator benchmark problem are presented to illustrate the offset-free tracking properties of the proposed approaches.