A preliminary result on frequency-shaped model predictive control

This paper introduces frequency-shaped model predictive control (FSMPC) by considering the cost function in the frequency domain, which applies for discrete-time linear systems. Borrowing from the idea of using Parseval´s theorem in the technique of the frequency-shaped LQR, we show that FSMPC can be formulated as a standard form of MPC. The terminal cost of the proposed FSMPC is chosen such that, when there are no state/input constraints, the optimal cost of FSMPC becomes the same as that of the frequency-shaped LQR, from which two benefits are obtained. That is, the closed-loop stability is straightforwardly achieved, and the performance of frequency-shaped LQR is inherited while state/input constraints are taken into account. A few examples are included to illustrate the effectiveness of the proposed FSMPC.