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A novel model predictive control (MPC) scheme that allows one to enforce hard constraints on the spectrum of a constrained system's output signal is presented. The approach is based on a time-local analysis of the spectrum of output signals by means of the short-time Fourier transform (STFT), and its squared magnitude, called the spectrogram. It is shown that an MPC problem with spectrogram constraints can be formulated as a quadratically constrained quadratic program (QCQP). We prove recursive feasibility and stability of the proposed spectrogram MPC scheme via an ellipsoidal invariant set, including spectrogram constraints. Moreover, it is pointed out how the proposed spectrogram MPC approach can be extended to MPC for tracking while ensuring recursive feasibility. Finally, we present simulation results of spectrogram MPC applied to a resonant system. Our simulations show that, by employing the proposed spectrogram MPC approach, oscillations can be attenuated in the system output, tracking a reference signal, by explicitly enforcing hard constraints on its spectrum. [ABSTRACT FROM PUBLISHER]

Well-known model predictive control (MPC) theory for constrained linear time-invariant (LTI) systems is extended to accommodate hard constraints and cost penalizations on the spectra of the system's output trajectories. Thus the proposed method facilitates enforcing constraints, and placing weights, on the harmonic content of input-, state- and output-trajectories, in addition to the usual constrained control objectives. The proposed methods are demonstrated by the example problem of reducing torsional vibrations in a drive-shaft. [ABSTRACT FROM PUBLISHER]