Constraint Removal for MPC with Performance Preservation and a Hyperthermia Cancer Treatment Case Study
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arXiv
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| Format: | Preprint |
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2024
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| author | Nouwens, S. A. N. de Jager, B. Paulides, M. M. Heemels, W. P. M. H. |
| author_facet | Nouwens, S. A. N. de Jager, B. Paulides, M. M. Heemels, W. P. M. H. |
| contents | Model predictive control (MPC) is an optimization-based control strategy with broad industrial adoption. Unfortunately, the required computation time to solve the receding-horizon MPC optimization problem can become prohibitively large for many applications with a large number of state constraints. This large number of state constraints can, for instance, originate from spatially discretizing a partial differential equation of which the solution has to satisfy constraints over the full spatial domain. This is particularly the case in MPC for RF-based hyperthermia cancer treatments, which forms a strong motivation for this study. To address this problem, we propose a novel constraint-adaptive MPC framework for linear discrete-time systems. In this framework, we select at each time-step a subset of the state constraints that are included in the optimization problem, thereby reducing the online computational burden. Critically, our framework guarantees the same closed-loop performance, recursive feasibility, and constraint satisfaction properties as the original (non-reduced) MPC scheme. We achieve this result by efficiently exploiting reachable set computations and the MPC cost function. We will demonstrate our novel method using a hyperthermia cancer treatment case study showing a two-orders of magnitude improvement in computation time, with identical closed-loop performance as the original (non-reduced) MPC scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17639 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Constraint Removal for MPC with Performance Preservation and a Hyperthermia Cancer Treatment Case Study Nouwens, S. A. N. de Jager, B. Paulides, M. M. Heemels, W. P. M. H. Systems and Control Optimization and Control Model predictive control (MPC) is an optimization-based control strategy with broad industrial adoption. Unfortunately, the required computation time to solve the receding-horizon MPC optimization problem can become prohibitively large for many applications with a large number of state constraints. This large number of state constraints can, for instance, originate from spatially discretizing a partial differential equation of which the solution has to satisfy constraints over the full spatial domain. This is particularly the case in MPC for RF-based hyperthermia cancer treatments, which forms a strong motivation for this study. To address this problem, we propose a novel constraint-adaptive MPC framework for linear discrete-time systems. In this framework, we select at each time-step a subset of the state constraints that are included in the optimization problem, thereby reducing the online computational burden. Critically, our framework guarantees the same closed-loop performance, recursive feasibility, and constraint satisfaction properties as the original (non-reduced) MPC scheme. We achieve this result by efficiently exploiting reachable set computations and the MPC cost function. We will demonstrate our novel method using a hyperthermia cancer treatment case study showing a two-orders of magnitude improvement in computation time, with identical closed-loop performance as the original (non-reduced) MPC scheme. |
| title | Constraint Removal for MPC with Performance Preservation and a Hyperthermia Cancer Treatment Case Study |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2410.17639 |