The Lyapunov Neural Network: Adaptive Stability Certification for Safe Learning of Dynamical Systems

Spencer M. Richards, Felix Berkenkamp, Andreas Krause
Proceedings of The 2nd Conference on Robot Learning, PMLR 87:466-476, 2018.

Abstract

Learning algorithms have shown considerable prowess in simulation by allowing robots to adapt to uncertain environments and improve their performance. However, such algorithms are rarely used in practice on safety-critical systems, since the learned policy typically does not yield any safety guarantees. That is, the required exploration may cause physical harm to the robot or its environment. In this paper, we present a method to learn accurate safety certificates for nonlinear, closed-loop dynamical systems. Specifically, we construct a neural network Lyapunov function and a training algorithm that adapts it to the shape of the largest safe region in the state space. The algorithm relies only on knowledge of inputs and outputs of the dynamics, rather than on any specific model structure. We demonstrate our method by learning the safe region of attraction for a simulated inverted pendulum. Furthermore, we discuss how our method can be used in safe learning algorithms together with statistical models of dynamical systems.

Cite this Paper

BibTeX
@InProceedings{pmlr-v87-richards18a, title = {The Lyapunov Neural Network: Adaptive Stability Certification for Safe Learning of Dynamical Systems}, author = {Richards, Spencer M. and Berkenkamp, Felix and Krause, Andreas}, booktitle = {Proceedings of The 2nd Conference on Robot Learning}, pages = {466--476}, year = {2018}, editor = {Billard, Aude and Dragan, Anca and Peters, Jan and Morimoto, Jun}, volume = {87}, series = {Proceedings of Machine Learning Research}, month = {29--31 Oct}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v87/richards18a/richards18a.pdf}, url = {https://proceedings.mlr.press/v87/richards18a.html}, abstract = {Learning algorithms have shown considerable prowess in simulation by allowing robots to adapt to uncertain environments and improve their performance. However, such algorithms are rarely used in practice on safety-critical systems, since the learned policy typically does not yield any safety guarantees. That is, the required exploration may cause physical harm to the robot or its environment. In this paper, we present a method to learn accurate safety certificates for nonlinear, closed-loop dynamical systems. Specifically, we construct a neural network Lyapunov function and a training algorithm that adapts it to the shape of the largest safe region in the state space. The algorithm relies only on knowledge of inputs and outputs of the dynamics, rather than on any specific model structure. We demonstrate our method by learning the safe region of attraction for a simulated inverted pendulum. Furthermore, we discuss how our method can be used in safe learning algorithms together with statistical models of dynamical systems. } }
Endnote
%0 Conference Paper %T The Lyapunov Neural Network: Adaptive Stability Certification for Safe Learning of Dynamical Systems %A Spencer M. Richards %A Felix Berkenkamp %A Andreas Krause %B Proceedings of The 2nd Conference on Robot Learning %C Proceedings of Machine Learning Research %D 2018 %E Aude Billard %E Anca Dragan %E Jan Peters %E Jun Morimoto %F pmlr-v87-richards18a %I PMLR %P 466--476 %U https://proceedings.mlr.press/v87/richards18a.html %V 87 %X Learning algorithms have shown considerable prowess in simulation by allowing robots to adapt to uncertain environments and improve their performance. However, such algorithms are rarely used in practice on safety-critical systems, since the learned policy typically does not yield any safety guarantees. That is, the required exploration may cause physical harm to the robot or its environment. In this paper, we present a method to learn accurate safety certificates for nonlinear, closed-loop dynamical systems. Specifically, we construct a neural network Lyapunov function and a training algorithm that adapts it to the shape of the largest safe region in the state space. The algorithm relies only on knowledge of inputs and outputs of the dynamics, rather than on any specific model structure. We demonstrate our method by learning the safe region of attraction for a simulated inverted pendulum. Furthermore, we discuss how our method can be used in safe learning algorithms together with statistical models of dynamical systems.
APA
Richards, S.M., Berkenkamp, F. & Krause, A.. (2018). The Lyapunov Neural Network: Adaptive Stability Certification for Safe Learning of Dynamical Systems. Proceedings of The 2nd Conference on Robot Learning, in Proceedings of Machine Learning Research 87:466-476 Available from https://proceedings.mlr.press/v87/richards18a.html.

Related Material