In Model Predictive Control (MPC) the control input is computed by solving a
constrained finite-time optimal control (CFTOC) problem at each sample in the
control loop. The main computational effort is often spent on computing the
search directions, which in MPC corresponds to solving unconstrained
finite-time optimal control (UFTOC) problems. This is commonly performed using
Riccati recursions or generic sparsity exploiting algorithms. In this work the
focus is efficient search direction computations for active-set (AS) type
methods. The system of equations to be solved at each AS iteration is changed
only by a low-rank modification of the previous one, and exploiting this
structured change is important for the performance of AS type solvers. In this
paper, theory for how to exploit these low-rank changes by modifying the
Riccati factorization between AS iterations in a structured way is presented. A
numerical evaluation of the proposed algorithm shows that the computation time
can be significantly reduced by modifying, instead of re-computing, the Riccati
factorization. This speed-up can be important for AS type solvers used for
linear, nonlinear and hybrid MPC