Data-driven optimal control of switched linear autonomous systems

Abstract

In this paper, a novel data-driven optimal control approach of switching times is proposed for unknown continuous-time switched linear autonomous systems with a finite-horizon cost function and a prescribed switching sequence. No a priori knowledge on the system dynamics is required in this approach. First, some formulas based on the Taylor expansion are deduced to estimate the derivatives of a cost function with respect to the switching times using system state data. Then, a data-driven optimal control approach based on the gradient decent algorithm is designed, taking advantage of the derivatives to approximate the optimal switching times. Moreover, the estimation errors are analysed and proven to be bounded. Finally, simulation examples are illustrated to validate the effectiveness of the approach.

Keywords:

• Data-driven control
• optimal control
• switching time
• switched linear systems
• autonomous systems

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Chi Zhang http://orcid.org/0000-0003-4029-8481

Minggang Gan http://orcid.org/0000-0002-2163-2475

Jingang Zhao http://orcid.org/0000-0002-2583-8446

Additional information

Funding

This work was supported by the National Natural Science Foundation of China under grant 61673065.

Notes on contributors

Chi Zhang

Chi Zhang received her B.E. degree in Automation in 2013 and M.E. degree in Control Engineering in 2015 from Beijing Institute of Technology, Beijing, China. She is currently a Ph.D. candidate in control science and engineering at Beijing Institute of Technology. Her main research interests include optimal control and switched systems.

Minggang Gan

Minggang Gan received his B.E. and Ph.D. degrees in Control Science and Engineering from Beijing Institute of Technology, Beijing, China, in 2001 and 2007, respectively. During 2015–2016, he was a visiting scholar in New York University. He is currently a Professor with the State Key Laboratory of Intelligent Control and Decision of Complex Systems, School of Automation, Beijing Institute of Technology, Member of IEEE. His main research interest covers intelligent information processing and intelligent control.

Jingang Zhao

Jingang Zhao received his B.E. degree in automation from Qingdao University of Technology, China in 2013, and M.E. degree in pattern recognition and intelligence system from Beijing Information Science and Technology University, China in 2016. He is currently working towards the Ph.D. degree at Beijing Institute of Technology, China. Since October 2018, he has been a Visiting Scholar with the Department of Electrical and Computer Engineering at The Ohio State University, United States. His research interests include optimal control, reinforcement learning and hybrid system.