2017/03/22 by Isak Nielsen, Nielsen, Isak, Daniel Axehill +1
Computer Science · Engineering · Mathematics · #Advanced Control Systems Optimization #Advanced Optimization Algorithms Research #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1703.07589
openalex publication_date 2017/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In Model Predictive Control (MPC) the control input is computed by solving a\nconstrained finite-time optimal control (CFTOC) problem at each sample in the\ncontrol loop. The main computational effort is often spent on computing the\nsearch directions, which in MPC corresponds to solving unconstrained\nfinite-time optimal control (UFTOC) problems. This is commonly performed using\nRiccati recursions or generic sparsity exploiting algorithms. In this work the\nfocus is efficient search direction computations for active-set (AS) type\nmethods. The system of equations to be solved at each AS iteration is changed\nonly by a low-rank modification of the previous one, and exploiting this\nstructured change is important for the performance of AS type solvers. In this\npaper, theory for how to exploit these low-rank changes by modifying the\nRiccati factorization between AS iterations in a structured way is presented. A\nnumerical evaluation of the proposed algorithm shows that the computation time\ncan be significantly reduced by modifying, instead of re-computing, the Riccati\nfactorization. This speed-up can be important for AS type solvers used for\nlinear, nonlinear and hybrid MPC.\n