A parallel structure exploiting factorization algorithm with applications to Model Predictive Control

In Model Predictive Control (MPC) the control signal is computed by solving a constrained finite-time optimal control (CFTOC) problem at each sample in the control loop. The CFTOC problem can be solved by, e.g., interior-point or active-set methods, where the main computational effort in both methods is known to be the computation of the search direction, i.e., the Newton step. This is often done using generic sparsity exploiting algorithms or serial Riccati recursions, but as parallel hardware is becoming more commonly available the need for parallel algorithms for computing the Newton step is increasing. In this paper a tailored, non-iterative parallel algorithm for computing the Newton step using the Riccati recursion is presented. The algorithm exploits the special structure of the Karush-Kuhn-Tucker system for a CFTOC problem. As a result it is possible to obtain logarithmic complexity growth in the prediction horizon length, which can be used to reduce the computation time for popular state-of-the-art MPC algorithms when applied to what is today considered as challenging control problems.