Reliably-stabilizing piecewise-affine neural network controllers
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866911947151114240 |
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| author | Fabiani, Filippo Goulart, Paul J. |
| author_facet | Fabiani, Filippo Goulart, Paul J. |
| contents | A common problem affecting neural network (NN) approximations of model predictive control (MPC) policies is the lack of analytical tools to assess the stability of the closed-loop system under the action of the NN-based controller. We present a general procedure to quantify the performance of such a controller, or to design minimum complexity NNs with rectified linear units (ReLUs) that preserve the desirable properties of a given MPC scheme. By quantifying the approximation error between NN-based and MPC-based state-to-input mappings, we first establish suitable conditions involving two key quantities, the worst-case error and the Lipschitz constant, guaranteeing the stability of the closed-loop system. We then develop an offline, mixed-integer optimization-based method to compute those quantities exactly. Together these techniques provide conditions sufficient to certify the stability and performance of a ReLU-based approximation of an MPC control law. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_07183 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Reliably-stabilizing piecewise-affine neural network controllers Fabiani, Filippo Goulart, Paul J. Systems and Control Machine Learning Optimization and Control A common problem affecting neural network (NN) approximations of model predictive control (MPC) policies is the lack of analytical tools to assess the stability of the closed-loop system under the action of the NN-based controller. We present a general procedure to quantify the performance of such a controller, or to design minimum complexity NNs with rectified linear units (ReLUs) that preserve the desirable properties of a given MPC scheme. By quantifying the approximation error between NN-based and MPC-based state-to-input mappings, we first establish suitable conditions involving two key quantities, the worst-case error and the Lipschitz constant, guaranteeing the stability of the closed-loop system. We then develop an offline, mixed-integer optimization-based method to compute those quantities exactly. Together these techniques provide conditions sufficient to certify the stability and performance of a ReLU-based approximation of an MPC control law. |
| title | Reliably-stabilizing piecewise-affine neural network controllers |
| topic | Systems and Control Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2111.07183 |