Robust stabilization of polytopic systems via fast and reliable neural network-based approximations
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866913295959588864 |
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| author | Fabiani, Filippo Goulart, Paul J. |
| author_facet | Fabiani, Filippo Goulart, Paul J. |
| contents | We consider the design of fast and reliable neural network (NN)-based approximations of traditional stabilizing controllers for linear systems with polytopic uncertainty, including control laws with variable structure and those based on a (minimal) selection policy. Building upon recent approaches for the design of reliable control surrogates with guaranteed structural properties, we develop a systematic procedure to certify the closed-loop stability and performance of a linear uncertain system when a trained rectified linear unit (ReLU)-based approximation replaces such traditional controllers. First, we provide a sufficient condition, which involves the worst-case approximation error between ReLU-based and traditional controller-based state-to-input mappings, ensuring that the system is ultimately bounded within a set with adjustable size and convergence rate. Then, we develop an offline, mixed-integer optimization-based method that allows us to compute that quantity exactly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_13209 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Robust stabilization of polytopic systems via fast and reliable neural network-based approximations Fabiani, Filippo Goulart, Paul J. Systems and Control Machine Learning Optimization and Control We consider the design of fast and reliable neural network (NN)-based approximations of traditional stabilizing controllers for linear systems with polytopic uncertainty, including control laws with variable structure and those based on a (minimal) selection policy. Building upon recent approaches for the design of reliable control surrogates with guaranteed structural properties, we develop a systematic procedure to certify the closed-loop stability and performance of a linear uncertain system when a trained rectified linear unit (ReLU)-based approximation replaces such traditional controllers. First, we provide a sufficient condition, which involves the worst-case approximation error between ReLU-based and traditional controller-based state-to-input mappings, ensuring that the system is ultimately bounded within a set with adjustable size and convergence rate. Then, we develop an offline, mixed-integer optimization-based method that allows us to compute that quantity exactly. |
| title | Robust stabilization of polytopic systems via fast and reliable neural network-based approximations |
| topic | Systems and Control Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2204.13209 |