Accelerating soft-constrained MPC for linear systems through online constraint removal
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| Format: | Preprint |
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2024
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| author | Nouwens, S. A. N. Paulides, M. M. Heemels, W. P. M. H. |
| author_facet | Nouwens, S. A. N. Paulides, M. M. Heemels, W. P. M. H. |
| contents | Optimization-based controllers, such as Model Predictive Control (MPC), have attracted significant research interest due to their intuitive concept, constraint handling capabilities, and natural application to multi-input multi-output systems. However, the computational complexity of solving a receding horizon problem at each time step remains a challenge for the deployment of MPC. This is particularly the case for systems constrained by many inequalities. Recently, we introduced the concept of constraint-adaptive MPC (ca-MPC) to address this challenge for linear systems with hard constraints. In ca-MPC, at each time step, a subset of the constraints is removed from the optimization problem, thereby accelerating the optimization procedure, while resulting in identical closed-loop behavior. The present paper extends this framework to soft-constrained MPC by detecting and removing constraints based on sub-optimal predicted input sequences, which is rather easy for soft-constrained MPC due to the receding horizon principle and the inclusion of slack variables. We will translate these new ideas explicitly to an offset-free output tracking problem. The effectiveness of these ideas is demonstrated on a two-dimensional thermal transport model, showing a three order of magnitude improvement in online computational time of the MPC scheme. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_17646 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Accelerating soft-constrained MPC for linear systems through online constraint removal Nouwens, S. A. N. Paulides, M. M. Heemels, W. P. M. H. Systems and Control Optimization-based controllers, such as Model Predictive Control (MPC), have attracted significant research interest due to their intuitive concept, constraint handling capabilities, and natural application to multi-input multi-output systems. However, the computational complexity of solving a receding horizon problem at each time step remains a challenge for the deployment of MPC. This is particularly the case for systems constrained by many inequalities. Recently, we introduced the concept of constraint-adaptive MPC (ca-MPC) to address this challenge for linear systems with hard constraints. In ca-MPC, at each time step, a subset of the constraints is removed from the optimization problem, thereby accelerating the optimization procedure, while resulting in identical closed-loop behavior. The present paper extends this framework to soft-constrained MPC by detecting and removing constraints based on sub-optimal predicted input sequences, which is rather easy for soft-constrained MPC due to the receding horizon principle and the inclusion of slack variables. We will translate these new ideas explicitly to an offset-free output tracking problem. The effectiveness of these ideas is demonstrated on a two-dimensional thermal transport model, showing a three order of magnitude improvement in online computational time of the MPC scheme. |
| title | Accelerating soft-constrained MPC for linear systems through online constraint removal |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2410.17646 |