A Parallel Riccati Factorization Algorithm with Applications to Model Predictive Control, Report no. LiTH-ISY-R-3078

Model Predictive Control (MPC) is increasing in popularity in industry as more e cient algorithms for solving the related optimization problem are developed. The main computational bottle-neck in on-line MPC is often the computation of the search step direction, i.e. the Newton step, which is often done using generic sparsity exploiting algorithms or Riccati recursions. However, as parallel hardware is becoming increasingly popular the demand for e cient parallel algorithms for solving the Newton step is increasing. In this paper a tailored, non-iterative parallel algorithm for computing the Riccati factorization is presented. The algorithm exploits the special structure in the MPC problem, and when su ciently many processing units are available, the complexity of the algorithm scales logarithmically in the prediction horizon. Computing the Newton step is the main computational bottle-neck in many MPC algorithms and the algorithm can signi cantly reduce the computation cost for popular state-of-the-art MPC algorithms.