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A Condensed and Sparse QP Formulation for Predictive Control


J.L. Jerez, E.C. Kerrigan, G. Constantinides

Conference on Decision and Control (CDC), Orlando, FL, USA, pp. 5217-5222

The computational burden that model predictive control (MPC) imposes depends to a large extent on the way the optimal control problem is formulated as an optimization problem. In this paper, we present a new formulation that results in a compact and sparse optimization problem to be solved at each sampling interval. The approach is based on a change of variables that leads to a block banded Hessian when the horizon length is bigger than the controllability index of the plant. In this case the problem can be solved with an interior-point method in time linear in the horizon length. Existing dense approaches grow cubically with the horizon length, whereas existing sparse approaches grow at a significantly greater rate than with the method presented here.


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% Autogenerated BibTeX entry
@InProceedings { JerKer:2011:IFA_4695,
    author={J.L. Jerez and E.C. Kerrigan and G. Constantinides},
    title={{A Condensed and Sparse QP Formulation for Predictive
    booktitle={Conference on Decision and Control (CDC)},
    address={Orlando, FL, USA},
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