A lifting approach to learning-based self-triggered control with Gaussian processes

Abstract

This paper investigates the design of self-triggered control for networked control systems (NCS), where the dynamics of the plant are initially unknown. Given the nature of the self-triggered control where state measurements are sent to the controller a-periodically, our proposal involves augmenting the continuous-time dynamics to a novel dynamical model that incorporates inter-event time as a supplemental input. Then, this new model is studied through Gaussian processes (GP) regression. Additionally, we propose a learning-based approach where a self-triggered controller is formulated by minimizing a cost function for the newly learned model, ensuring consideration of inter-sample behavior. The usage of the lifting approach facilitates the application of gradient-based policy updates, allowing for the effective optimization of both control and communication policies. Finally, we provide a numerical simulation to illustrate the effectiveness of the proposed approach.

GRAPHICAL ABSTRACT

Keywords:

• Event-triggered and self-triggered control
• Gaussian process regression
• optimal control

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Here, ${\tau }_{max}$ could be selected arbitrary large so as to lengthen the inter-event time.

Additional information

Funding

This work is partially supported by Japan Science and Technology Agency (JST) CREST [grant number JPMJCR2012], Japan Science and Technology Agency (JST) ACT-X [grant number JPMJAX23CK], and Japan Society for the Promotion of Science (JSPS) KAKENHI [grant numbers 21K14184, 23KJ1451, and 22KK0155]; Japan Science and Technology Agency [grant number JPMJMS2281].

Notes on contributors

Wang Zhijun

Wang Zhijun received the M.E degree from Osaka University, Japan in 2023. His research interest include model predictive control, networked control systems and machine learning.

Kazumune Hashimoto

Kazumune Hashimoto received the first M.E. degree from the KTH Royal Institute of Technology, Sweden, in 2014, and the second M.E. degree and the Ph.D. degree from Keio University, Japan, in 2015 and 2018, respectively. From 2018 to 2020, he was a Postdoctoral Researcher with the KTH Royal Institute of Technology, Sweden, and Osaka University, Japan. Currently, he is a lecturer at Osaka University, Japan. His research interests include model predictive control, networked control systems, and formal methods for control theory.

Wataru Hashimoto

Wataru Hashimoto received the M.E degree from Osaka University, Japan in 2021. Currently, his is a PhD student at Osaka University, Japan. His research interest include model predictive control and machine learning.

Shigemasa Takai

Shigemasa Takai received the B.E.and M.E. degrees from Kobe University, Kobe, Japan, in 1989 and 1991, respectively, and the Ph.D. degree from Osaka University, Suita, Japan, in 1995.From 1992 to 1998, he was a Research Associate with Osaka University. In 1998, he joined Wakayama University, Wakayama, Japan, as a Lecturer, and became an Associate Professor in 1999. From 2004 to 2009, he was an Associate Professor with Kyoto Institute of Technology, Kyoto, Japan. Since 2009, he has been a Professor with Osaka University, Suita, Japan. His research interests include supervisory control and fault diagnosis of discrete event systems.