Stability Analysis and Controller Synthesis using Single-hidden-layer ReLU Neural Networks

Pouya Samanipour, Hasan A. Poonawala

Research output: Contribution to journalArticlepeer-review


This paper presents algorithms to solve analysis and controller synthesis problems for dynamical systems modeled as a recurrent single-hidden-layer rectified linear unit neural network (ReLU NN), or equivalently, a piecewise affine dynamical system. Such models are interesting since they may arise through the use of modern machine learning methods for system identification, or as closed-loop solutions in certain classes of model predictive control (MPC) problems. A key idea in the proposed approach is to use piecewise affine Lyapunov functions parametrized as ReLU neural networks, and similarly parametrized controllers. This compatible representation between the Lyapunov function and the dynamics simplifies the automation of analysis of and controller synthesis for learned models. Our method of verifying a candidate Lyapunov function is faster than methods based on mixed integer programming. We ‘learn’ controllers and Lyapunov functions using both weight updates and network architecture search, without gradients. We demonstrate the proposed algorithm on examples involving learned models, explicit MPC controllers, and constrained controller synthesis.

Original languageEnglish
Pages (from-to)1-12
Number of pages12
JournalIEEE Transactions on Automatic Control
StateAccepted/In press - 2023

Bibliographical note

Publisher Copyright:


  • Analytical models
  • Artificial neural networks
  • Dynamical systems
  • Lyapunov methods
  • Neural networks
  • Optimization
  • Search problems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


Dive into the research topics of 'Stability Analysis and Controller Synthesis using Single-hidden-layer ReLU Neural Networks'. Together they form a unique fingerprint.

Cite this