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Single harmonic based Model Predictive Control for tracking

One of the challenges of model predictive control is achieving a large domain of attraction with a small prediction horizon, in order to reduce the computation time and ease its implementation in embedded platforms. The domain of attraction can be enlarged by increasing the prediction horizon, at the expense of an increase in the number of decision variables, or by enlarging the terminal set. In MPC for tracking the terminal set is enlarged by the addition of an artificial equilibrium point as a decision variable, while maintaining stability of the closed loop system. In this paper we propose an extension of the MPC for tracking formulation that adds a single harmonic signal as an artificial reference. We show that a significant increase of the domain of attraction is achieved with the addition of a low number of decision variables, especially for low values of the prediction horizon.