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Robust stabilization of polytopic systems via fast and reliable neural network‐based approximations.
- Source :
-
International Journal of Robust & Nonlinear Control . Jun2024, Vol. 34 Issue 9, p6180-6201. 22p. - Publication Year :
- 2024
-
Abstract
- We consider the design of fast and reliable neural network‐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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *LINEAR systems
*UNCERTAIN systems
*APPROXIMATION error
*ROBUST control
Subjects
Details
- Language :
- English
- ISSN :
- 10498923
- Volume :
- 34
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- International Journal of Robust & Nonlinear Control
- Publication Type :
- Academic Journal
- Accession number :
- 177114689
- Full Text :
- https://doi.org/10.1002/rnc.7315