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Model predictive control (MPC) for linear dynamical systems requires solvingan optimal control structured quadratic program (QP) at each sampling instant.This paper proposes a primal active-set strategy (PRESAS) for the efficientsolution of such block-sparse QPs, based on a preconditioned iterative solverto compute the search direction in each iteration. Rank-one factorizationupdates of the preconditioner result in a per-iteration computationalcomplexity of $\mathcal{O}(N m^2)$, where $m$ denotes the number of state andcontrol variables and $N$ the number of control intervals. Three differentblock-structured preconditioning techniques are presented and their numericalproperties are studied further. In addition, an augmented Lagrangian basedimplementation is proposed to avoid a costly initialization procedure to find aprimal feasible starting point. Based on a standalone C code implementation, weillustrate the computational performance of PRESAS against current state of theart QP solvers for multiple linear and nonlinear MPC case studies. We also showthat the solver is real-time feasible on a dSPACE MicroAutoBox-II rapidprototyping unit for vehicle control applications, and numerical reliability isillustrated based on experimental results from a testbench of small-scaleautonomous vehicles.

PRESAS: Block-Structured Preconditioning of Iterative Solvers within a Primal Active-Set Method for fast MPC