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Spectrogram-MPC: Enforcing hard constraints on systems' output spectra


Jean-Hubert Hours, M.N. Zeilinger, R. Gondhalekar, C.N. Jones

American Control Conference, Montreal, Canada

A novel model predictive control (MPC) scheme that allows one to enforce hard constraints on the spectrum of a constrained systemís 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). 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, the proposed method is 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 oscillations can be removed from the tracking signal by explicitly enforcing hard constraints on its spectrum in an MPC scheme.


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% Autogenerated BibTeX entry
@InProceedings { HouEtal:2012:IFA_4000,
    author={Jean-Hubert Hours and M.N. Zeilinger and R. Gondhalekar and C.N.
    title={{Spectrogram-MPC: Enforcing hard constraints on systems'
	  output spectra}},
    booktitle={American Control Conference},
    address={Montreal, Canada},
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