Banded null basis and ADMM for embedded MPC
In this paper, we propose an improved QP solver for embedded implementations of MPC controllers. We adopt a “reduced Hessian” approach for handling the equality constraints that arise in the well-known “banded” formulation of MPC (in which the predicted states are not eliminated). Our key observatio...
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| Format: | Journal Article |
| Language: | English |
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2018
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| Online Access: | https://hdl.handle.net/10356/89779 http://hdl.handle.net/10220/47137 |
| _version_ | 1811688343222616064 |
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| author | Dang, Thuy V Ling, Keck Voon Maciejowski, Jan |
| author2 | School of Electrical and Electronic Engineering |
| author_facet | School of Electrical and Electronic Engineering Dang, Thuy V Ling, Keck Voon Maciejowski, Jan |
| author_sort | Dang, Thuy V |
| collection | NTU |
| description | In this paper, we propose an improved QP solver for embedded implementations of MPC controllers. We adopt a “reduced Hessian” approach for handling the equality constraints that arise in the well-known “banded” formulation of MPC (in which the predicted states are not eliminated). Our key observation is that a banded basis exists for the null space of the banded equality-constraint matrix, and that this leads to a QP of the same size as the “condensed” formulation of MPC problems, which is considerably smaller than the “banded” formulation. We use the Alternating Direction Method of Multipliers (ADMM) - which is known to be particularly suitable for embedded implementations - to solve this smaller QP problem. Our C implementation results for a particular MPC example (a 9-state, 3-input quadrotor) show that our proposed algorithm is about 4 times faster than an existing well-performing ADMM variant (“indirect indicator” ADMM or “iiADMM”) and 3 times faster than the well-known QP solver CVXGEN. The convergence rate and code size of the proposed ADMM variant is also comparable with iiADMM. |
| first_indexed | 2024-10-01T05:30:42Z |
| format | Journal Article |
| id | ntu-10356/89779 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T05:30:42Z |
| publishDate | 2018 |
| record_format | dspace |
| spelling | ntu-10356/897792020-03-07T13:57:29Z Banded null basis and ADMM for embedded MPC Dang, Thuy V Ling, Keck Voon Maciejowski, Jan School of Electrical and Electronic Engineering Interdisciplinary Graduate School (IGS) DRNTU::Engineering::Electrical and electronic engineering ADMM Banded Null Basis In this paper, we propose an improved QP solver for embedded implementations of MPC controllers. We adopt a “reduced Hessian” approach for handling the equality constraints that arise in the well-known “banded” formulation of MPC (in which the predicted states are not eliminated). Our key observation is that a banded basis exists for the null space of the banded equality-constraint matrix, and that this leads to a QP of the same size as the “condensed” formulation of MPC problems, which is considerably smaller than the “banded” formulation. We use the Alternating Direction Method of Multipliers (ADMM) - which is known to be particularly suitable for embedded implementations - to solve this smaller QP problem. Our C implementation results for a particular MPC example (a 9-state, 3-input quadrotor) show that our proposed algorithm is about 4 times faster than an existing well-performing ADMM variant (“indirect indicator” ADMM or “iiADMM”) and 3 times faster than the well-known QP solver CVXGEN. The convergence rate and code size of the proposed ADMM variant is also comparable with iiADMM. NRF (Natl Research Foundation, S’pore) Published version 2018-12-20T09:03:01Z 2019-12-06T17:33:18Z 2018-12-20T09:03:01Z 2019-12-06T17:33:18Z 2017 Journal Article Dang, T. V., Ling, K. V., & Maciejowski, J. (2017). Banded null basis and ADMM for embedded MPC. IFAC-PapersOnLine, 50(1), 13170-13175. doi: 10.1016/j.ifacol.2017.08.2172 2405-8963 https://hdl.handle.net/10356/89779 http://hdl.handle.net/10220/47137 10.1016/j.ifacol.2017.08.2172 en IFAC-PapersOnLine © IFAC 2018. This work is posted here by permission of IFAC for your personal use. Not for distribution. The original version was published in ifac-papersonline.net, DOI: 10.1016/j.ifacol.2017.08.2172. 6 p. application/pdf |
| spellingShingle | DRNTU::Engineering::Electrical and electronic engineering ADMM Banded Null Basis Dang, Thuy V Ling, Keck Voon Maciejowski, Jan Banded null basis and ADMM for embedded MPC |
| title | Banded null basis and ADMM for embedded MPC |
| title_full | Banded null basis and ADMM for embedded MPC |
| title_fullStr | Banded null basis and ADMM for embedded MPC |
| title_full_unstemmed | Banded null basis and ADMM for embedded MPC |
| title_short | Banded null basis and ADMM for embedded MPC |
| title_sort | banded null basis and admm for embedded mpc |
| topic | DRNTU::Engineering::Electrical and electronic engineering ADMM Banded Null Basis |
| url | https://hdl.handle.net/10356/89779 http://hdl.handle.net/10220/47137 |
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