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Verification of Closed-loop Systems with Neural Network Controllers

10 pagesPublished: May 25, 2019


This benchmark suite presents a detailed description of a series of closed-loop control systems with artificial neural network controllers. In many applications, feed-forward neural networks are heavily involved in the implementation of controllers by learning and representing control laws through several methods such as model predictive control (MPC) and reinforcement learning (RL). The type of networks that we consider in this manuscript are feed-forward neural networks consisting of multiple hidden layers with ReLU activation functions and a linear activation function in the output layer. While neural network con- trollers have been able to achieve desirable performance in many contexts, they also present a unique challenge in that it is difficult to provide any guarantees about the correctness of their behavior or reason about the stability a system that employs their use. Thus, from a controls perspective, it is necessary to verify them in conjunction with their corresponding plants in closed-loop. While there have been a handful of works proposed towards the verification of closed-loop systems with feed-forward neural network controllers, this area still lacks attention and a unified set of benchmark examples on which verification techniques can be evaluated and compared. Thus, to this end, we present a range of closed-loop control systems ranging from two to six state variables, and a range of controllers with sizes in the range of eleven neurons to a few hundred neurons in more complex systems.

Keyphrases: closed-loop system, control systems, neural network controller, verification benchmark

In: Goran Frehse and Matthias Althoff (editors). ARCH19. 6th International Workshop on Applied Verification of Continuous and Hybrid Systems, vol 61, pages 201--210

BibTeX entry
  author    = {Diego Manzanas Lopez and Patrick Musau and Hoang-Dung Tran and Taylor T. Johnson},
  title     = {Verification of Closed-loop Systems with Neural Network Controllers},
  booktitle = {ARCH19. 6th International Workshop on Applied Verification of Continuous and Hybrid Systems},
  editor    = {Goran Frehse and Matthias Althoff},
  series    = {EPiC Series in Computing},
  volume    = {61},
  pages     = {201--210},
  year      = {2019},
  publisher = {EasyChair},
  bibsource = {EasyChair,},
  issn      = {2398-7340},
  url       = {},
  doi       = {10.29007/btv1}}
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