A sparse ADMM-based solver for linear MPC subject to terminal quadratic constraint
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866911858382864384 |
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| author | Krupa, Pablo Jaouani, Rim Limon, Daniel Alamo, Teodoro |
| author_facet | Krupa, Pablo Jaouani, Rim Limon, Daniel Alamo, Teodoro |
| contents | Model Predictive Control (MPC) typically includes a terminal constraint to guarantee stability of the closed-loop system under nominal conditions. In linear MPC this constraint is generally taken on a polyhedral set, leading to a quadratic optimization problem. However, the use of an ellipsoidal terminal constraint may be desirable, leading to an optimization problem with a quadratic constraint. In this case, the optimization problem can be solved using Second Order Cone (SOC) programming solvers, since the quadratic constraint can be posed as a SOC constraint, at the expense of adding additional slack variables and possibly compromising the simple structure of the solver ingredients. In this paper we present a sparse solver for linear MPC subject to a terminal ellipsoidal constraint based on the alternating direction method of multipliers algorithm in which we directly deal with the quadratic constraints without having to resort to the use of a SOC constraint nor the inclusion of additional decision variables. The solver is suitable for its use in embedded systems, since it is sparse, has a small memory footprint and requires no external libraries. We compare its performance against other approaches from the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_08419 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A sparse ADMM-based solver for linear MPC subject to terminal quadratic constraint Krupa, Pablo Jaouani, Rim Limon, Daniel Alamo, Teodoro Optimization and Control Systems and Control Model Predictive Control (MPC) typically includes a terminal constraint to guarantee stability of the closed-loop system under nominal conditions. In linear MPC this constraint is generally taken on a polyhedral set, leading to a quadratic optimization problem. However, the use of an ellipsoidal terminal constraint may be desirable, leading to an optimization problem with a quadratic constraint. In this case, the optimization problem can be solved using Second Order Cone (SOC) programming solvers, since the quadratic constraint can be posed as a SOC constraint, at the expense of adding additional slack variables and possibly compromising the simple structure of the solver ingredients. In this paper we present a sparse solver for linear MPC subject to a terminal ellipsoidal constraint based on the alternating direction method of multipliers algorithm in which we directly deal with the quadratic constraints without having to resort to the use of a SOC constraint nor the inclusion of additional decision variables. The solver is suitable for its use in embedded systems, since it is sparse, has a small memory footprint and requires no external libraries. We compare its performance against other approaches from the literature. |
| title | A sparse ADMM-based solver for linear MPC subject to terminal quadratic constraint |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2105.08419 |