Safe Control with Neural Network Dynamic Models

Tianhao Wei, Changliu Liu
Proceedings of The 4th Annual Learning for Dynamics and Control Conference, PMLR 168:739-750, 2022.

Abstract

Safety is critical in autonomous robotic systems. A safe control law should ensure forward invariance of a safe set (a subset in the state space). It has been extensively studied regarding how to derive a safe control law with a control-affine analytical dynamic model. However, how to formally derive a safe control law with Neural Network Dynamic Models (NNDM) remains unclear due to the lack of computationally tractable methods to deal with these black-box functions. In fact, even finding the control that minimizes an objective for NNDM without any safety constraint is still challenging. In this work, we propose MIND-SIS (Mixed Integer for Neural network Dynamic model with Safety Index Synthesis), the first method to synthesize safe control for NNDM. The method includes two parts: 1) SIS: an algorithm for the offline synthesis of the safety index (also called as a barrier function), which uses evolutionary methods and 2) MIND: an algorithm for online computation of the optimal and safe control signal, which solves a constrained optimization using a computationally efficient encoding of neural networks. It has been theoretically proved that MIND-SIS guarantees forward invariance and finite convergence to a subset of the user-defined safe set. And it has been numerically validated that MIND-SIS achieves safe and optimal control of NNDM. The optimality gap is less than $10^{-8}$, and the safety constraint violation is $0$.

Cite this Paper

BibTeX
@InProceedings{pmlr-v168-wei22a, title = {Safe Control with Neural Network Dynamic Models}, author = {Wei, Tianhao and Liu, Changliu}, booktitle = {Proceedings of The 4th Annual Learning for Dynamics and Control Conference}, pages = {739--750}, year = {2022}, editor = {Firoozi, Roya and Mehr, Negar and Yel, Esen and Antonova, Rika and Bohg, Jeannette and Schwager, Mac and Kochenderfer, Mykel}, volume = {168}, series = {Proceedings of Machine Learning Research}, month = {23--24 Jun}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v168/wei22a/wei22a.pdf}, url = {https://proceedings.mlr.press/v168/wei22a.html}, abstract = {Safety is critical in autonomous robotic systems. A safe control law should ensure forward invariance of a safe set (a subset in the state space). It has been extensively studied regarding how to derive a safe control law with a control-affine analytical dynamic model. However, how to formally derive a safe control law with Neural Network Dynamic Models (NNDM) remains unclear due to the lack of computationally tractable methods to deal with these black-box functions. In fact, even finding the control that minimizes an objective for NNDM without any safety constraint is still challenging. In this work, we propose MIND-SIS (Mixed Integer for Neural network Dynamic model with Safety Index Synthesis), the first method to synthesize safe control for NNDM. The method includes two parts: 1) SIS: an algorithm for the offline synthesis of the safety index (also called as a barrier function), which uses evolutionary methods and 2) MIND: an algorithm for online computation of the optimal and safe control signal, which solves a constrained optimization using a computationally efficient encoding of neural networks. It has been theoretically proved that MIND-SIS guarantees forward invariance and finite convergence to a subset of the user-defined safe set. And it has been numerically validated that MIND-SIS achieves safe and optimal control of NNDM. The optimality gap is less than $10^{-8}$, and the safety constraint violation is $0$.} }
Endnote
%0 Conference Paper %T Safe Control with Neural Network Dynamic Models %A Tianhao Wei %A Changliu Liu %B Proceedings of The 4th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2022 %E Roya Firoozi %E Negar Mehr %E Esen Yel %E Rika Antonova %E Jeannette Bohg %E Mac Schwager %E Mykel Kochenderfer %F pmlr-v168-wei22a %I PMLR %P 739--750 %U https://proceedings.mlr.press/v168/wei22a.html %V 168 %X Safety is critical in autonomous robotic systems. A safe control law should ensure forward invariance of a safe set (a subset in the state space). It has been extensively studied regarding how to derive a safe control law with a control-affine analytical dynamic model. However, how to formally derive a safe control law with Neural Network Dynamic Models (NNDM) remains unclear due to the lack of computationally tractable methods to deal with these black-box functions. In fact, even finding the control that minimizes an objective for NNDM without any safety constraint is still challenging. In this work, we propose MIND-SIS (Mixed Integer for Neural network Dynamic model with Safety Index Synthesis), the first method to synthesize safe control for NNDM. The method includes two parts: 1) SIS: an algorithm for the offline synthesis of the safety index (also called as a barrier function), which uses evolutionary methods and 2) MIND: an algorithm for online computation of the optimal and safe control signal, which solves a constrained optimization using a computationally efficient encoding of neural networks. It has been theoretically proved that MIND-SIS guarantees forward invariance and finite convergence to a subset of the user-defined safe set. And it has been numerically validated that MIND-SIS achieves safe and optimal control of NNDM. The optimality gap is less than $10^{-8}$, and the safety constraint violation is $0$.
APA
Wei, T. & Liu, C.. (2022). Safe Control with Neural Network Dynamic Models. Proceedings of The 4th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 168:739-750 Available from https://proceedings.mlr.press/v168/wei22a.html.

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