Fast MPC with staircase parametrization of the inputs: Continuous input blocking

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In this paper we present a new method to reduce the computational complexity of model predictive control algorithms with online optimization. The formulation of the predictive equations is performed in the continuous-time domain, while the control inputs are parametrized as piecewise constant functions, with less steps than the control horizon. The continuous-time formulation permits the arbitrary choice of the prediction and control time-instants, disregarding the sampling period of the system, and this improves the goodness of the approximation. Moreover, since the inputs are forced to be piecewise constant, the resulting controller can be directly implemented in discretetime. A tuning method for the choice of the prediction and control instants is proposed, minimizing the deviation with respect to the non-approximated controller. Numerical results show the effectiveness of this strategy against other methods with same reduction of computational complexity.