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Low-Rank Modifications of Riccati Factorizations for Model Predictive Control
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0001-6957-2603
2018 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 63, no 3, p. 872-879Article in journal (Refereed) Published
Abstract [en]

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 when solving the CFTOC problem using an active-set (AS) method 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 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.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2018. Vol. 63, no 3, p. 872-879
Keywords [en]
Indexes; Linear matrix inequalities; Optimal control; Optimization; Predictive control; Search problems; Sparse matrices; MPC; Riccati recursion; low-rank; optimization
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-142894DOI: 10.1109/TAC.2017.2737228ISI: 000426276500025OAI: oai:DiVA.org:liu-142894DiVA, id: diva2:1155701
Available from: 2017-11-09 Created: 2017-11-09 Last updated: 2018-03-20Bibliographically approved

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