TY - GEN
T1 - Reachable Set Estimation and Safety Verification for Piecewise Linear Systems with Neural Network Controllers
AU - Xiang, Weiming
AU - Tran, Hoang Dung
AU - Rosenfeld, Joel A.
AU - Johnson, Taylor T.
N1 - Funding Information:
The material presented in this paper is based upon work supported by the National Science Foundation (NSF) under grant numbers CNS 1464311 and 1713253, and SHF 1527398 and 1736323, and the Air Force Office of Scientific Research (AFOSR) under contract numbers FA9550-15-1-0258, FA9550-16-1-0246, and FA9550-18-1-0122. The U.S. government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of AFOSR or NSF.
PY - 2018/8/9
Y1 - 2018/8/9
N2 - In this work, the reachable set estimation and safety verification problems for a class of piecewise linear systems equipped with neural network controllers are addressed. The neural network is considered to consist of Rectified Linear Unit (ReLU) activation functions. A layer-by-layer approach is developed for the output reachable set computation of ReLU neural networks. The computation is formulated in the form of a set of manipulations for a union of polytopes. Based on the output reachable set for neural network controllers, the output reachable set for a piecewise linear feedback control system can be estimated iteratively for a given finite-time interval. With the estimated output reachable set, the safety verification for piecewise linear systems with neural network controllers can be performed by checking the existence of intersections of unsafe regions and output reach set. A numerical example is presented to illustrate the effectiveness of our approach.
AB - In this work, the reachable set estimation and safety verification problems for a class of piecewise linear systems equipped with neural network controllers are addressed. The neural network is considered to consist of Rectified Linear Unit (ReLU) activation functions. A layer-by-layer approach is developed for the output reachable set computation of ReLU neural networks. The computation is formulated in the form of a set of manipulations for a union of polytopes. Based on the output reachable set for neural network controllers, the output reachable set for a piecewise linear feedback control system can be estimated iteratively for a given finite-time interval. With the estimated output reachable set, the safety verification for piecewise linear systems with neural network controllers can be performed by checking the existence of intersections of unsafe regions and output reach set. A numerical example is presented to illustrate the effectiveness of our approach.
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U2 - 10.23919/ACC.2018.8431048
DO - 10.23919/ACC.2018.8431048
M3 - Conference contribution
AN - SCOPUS:85052602200
SN - 9781538654286
T3 - Proceedings of the American Control Conference
SP - 1574
EP - 1579
BT - 2018 Annual American Control Conference, ACC 2018
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2018 Annual American Control Conference, ACC 2018
Y2 - 27 June 2018 through 29 June 2018
ER -