Neural network controllers for uncertain linear systems

Filippo Fabiani and Paul J. Goulart

@misc{FG:2022,
  author = {Filippo Fabiani and Paul J. Goulart},
  title = {Neural network controllers for uncertain linear systems},
  year = {2022}
}

We consider the design of reliable neural network (NN)-based approximations of traditional stabilizing controllers for linear systems affected by polytopic uncertainty, including controllers with variable structure and those based on a minimal selection policy. We develop a systematic procedure to certify the closed-loop stability and performance of a polytopic system when a rectified linear unit (ReLU)-based approximation replaces such traditional controllers. We provide sufficient conditions to ensure stability involving the worst-case approximation error and the Lipschitz constant characterizing the error function between ReLU-based and traditional controller-based state-to-input mappings, and further provide offline, mixed-integer optimization-based methods that allow us to compute those quantities exactly.