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Linear Model Predictive Control (MPC) is a widely used method to controlsystems with linear dynamics. Efficient interior-point methods have beenproposed which leverage the block diagonal structure of the quadratic program(QP) resulting from the receding horizon control formulation. However, theyrequire two matrix factorizations per interior-point method iteration, one eachfor the computation of the dual and the primal. Recently though an interiorpoint method based on the null-space method has been proposed which requiresonly a single decomposition per iteration. While the then used null-space basisleads to dense null-space projections, in this work we propose a sparsenull-space basis which preserves the block diagonal structure of the MPCmatrices. Since it is based on the inverse of the transfer matrix we introducethe notion of so-called virtual controls which enables just that invertibility.A combination of the reduced number of factorizations and omission of theevaluation of the dual lets our solver outperform others in terms ofcomputational speed by an increasing margin dependent on the number of stateand control variables.

$\mathcal{N}$IPM-MPC: An Efficient Null-Space Method Based Interior-Point Method for Model Predictive Control