Efficient computation of Lipschitz constants for MPC with symmetries
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866910519115382784 |
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| author | Teichrib, Dieter Darup, Moritz Schulze |
| author_facet | Teichrib, Dieter Darup, Moritz Schulze |
| contents | Lipschitz constants for linear MPC are useful for certifying inherent robustness against unmodeled disturbances or robustness for neural network-based approximations of the control law. In both cases, knowing the minimum Lipschitz constant leads to less conservative certifications. Computing this minimum Lipschitz constant is trivial given the explicit MPC. However, the computation of the explicit MPC may be intractable for complex systems. The paper discusses a method for efficiently computing the minimum Lipschitz constant without using the explicit control law. The proposed method simplifies a recently presented mixed-integer linear program (MILP) that computes the minimum Lipschitz constant. The simplification is obtained by exploiting saturation and symmetries of the control law and irrelevant constraints of the optimal control problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_04580 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Efficient computation of Lipschitz constants for MPC with symmetries Teichrib, Dieter Darup, Moritz Schulze Optimization and Control Systems and Control Lipschitz constants for linear MPC are useful for certifying inherent robustness against unmodeled disturbances or robustness for neural network-based approximations of the control law. In both cases, knowing the minimum Lipschitz constant leads to less conservative certifications. Computing this minimum Lipschitz constant is trivial given the explicit MPC. However, the computation of the explicit MPC may be intractable for complex systems. The paper discusses a method for efficiently computing the minimum Lipschitz constant without using the explicit control law. The proposed method simplifies a recently presented mixed-integer linear program (MILP) that computes the minimum Lipschitz constant. The simplification is obtained by exploiting saturation and symmetries of the control law and irrelevant constraints of the optimal control problem. |
| title | Efficient computation of Lipschitz constants for MPC with symmetries |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2311.04580 |