Robust stabilization of polytopic systems via fast and reliable neural network-based approximations
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Abstract (arXiv)
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.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 14 of its 57 references that are in the map. First posted on arXiv 27 Apr 2022.
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14 of 57 references.
References · 14
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- 2020Stability and feasibility of neural network-based controllers via output range analysiscited by 10
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