Formal Synthesis of Safety Controllers for Unknown Stochastic Control Systems using Gaussian Process Learning

Rameez Wajid, Asad Ullah Awan, Majid Zamani
Proceedings of The 4th Annual Learning for Dynamics and Control Conference, PMLR 168:624-636, 2022.

Abstract

Formal synthesis of controllers for stochastic control systems with unknown models is a challenging problem. In this paper, we focus on safety controller synthesis for nonlinear stochastic control systems. The approach consists of a learning step followed by a controller synthesis scheme using control barrier functions. In the learning phase, we employ Gaussian processes (GP) to learn models of unknown stochastic control systems in the presence of both process and measurement noises. In the controller synthesis phase, we compute control barrier functions together with their corresponding controllers based on the learned GP and quantify lower bounds on the probabilities of safety satisfaction for the original unknown systems equipped with the synthesized controllers. Finally, the effectiveness of the proposed approach is illustrated on a room temperature control and a vehicle lane-keeping example.

Cite this Paper

BibTeX
@InProceedings{pmlr-v168-wajid22a, title = {Formal Synthesis of Safety Controllers for Unknown Stochastic Control Systems using Gaussian Process Learning}, author = {Wajid, Rameez and Awan, Asad Ullah and Zamani, Majid}, booktitle = {Proceedings of The 4th Annual Learning for Dynamics and Control Conference}, pages = {624--636}, 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/wajid22a/wajid22a.pdf}, url = {https://proceedings.mlr.press/v168/wajid22a.html}, abstract = {Formal synthesis of controllers for stochastic control systems with unknown models is a challenging problem. In this paper, we focus on safety controller synthesis for nonlinear stochastic control systems. The approach consists of a learning step followed by a controller synthesis scheme using control barrier functions. In the learning phase, we employ Gaussian processes (GP) to learn models of unknown stochastic control systems in the presence of both process and measurement noises. In the controller synthesis phase, we compute control barrier functions together with their corresponding controllers based on the learned GP and quantify lower bounds on the probabilities of safety satisfaction for the original unknown systems equipped with the synthesized controllers. Finally, the effectiveness of the proposed approach is illustrated on a room temperature control and a vehicle lane-keeping example.} }
Endnote
%0 Conference Paper %T Formal Synthesis of Safety Controllers for Unknown Stochastic Control Systems using Gaussian Process Learning %A Rameez Wajid %A Asad Ullah Awan %A Majid Zamani %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-wajid22a %I PMLR %P 624--636 %U https://proceedings.mlr.press/v168/wajid22a.html %V 168 %X Formal synthesis of controllers for stochastic control systems with unknown models is a challenging problem. In this paper, we focus on safety controller synthesis for nonlinear stochastic control systems. The approach consists of a learning step followed by a controller synthesis scheme using control barrier functions. In the learning phase, we employ Gaussian processes (GP) to learn models of unknown stochastic control systems in the presence of both process and measurement noises. In the controller synthesis phase, we compute control barrier functions together with their corresponding controllers based on the learned GP and quantify lower bounds on the probabilities of safety satisfaction for the original unknown systems equipped with the synthesized controllers. Finally, the effectiveness of the proposed approach is illustrated on a room temperature control and a vehicle lane-keeping example.
APA
Wajid, R., Awan, A.U. & Zamani, M.. (2022). Formal Synthesis of Safety Controllers for Unknown Stochastic Control Systems using Gaussian Process Learning. Proceedings of The 4th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 168:624-636 Available from https://proceedings.mlr.press/v168/wajid22a.html.

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