Distributed LQR control for discrete-time homogeneous systems

ABSTRACT

This paper investigates the distributed linear quadratic regulation (LQR) controller design method for discrete-time homogeneous scalar systems. Based on the optimal centralised control theory, the existence condition for distributed optimal controller is firstly proposed. It shows that the globally optimal distributed controller is dependent on the structure of the penalty matrix. Such results can be used in consensus problems and used to find under which communication topology (may not be an all-to-all form) the optimal distributed controller exists. When the proposed condition cannot hold, a suboptimal design method with the aid of the decomposition of discrete algebraic Riccati equations and robustness of local controllers is proposed. The computation complexity and communication load for each subsystem are only dependent on the number of its neighbours.

Keywords:

• Distributed linear quadratic regulation
• scalar identical subsystem
• distributed controller design
• suboptimal controller design
• robust stability

Acknowledgements

The authors sincerely appreciate associate editor and the anonymous reviewers for their valuable comments and constructive suggestions to improve the presentation of this paper. This work was supported by the National Natural Science Foundation of China (Grant Nos. 61573220, 61473134, 61304045), and the Scientific Research Foundation for Outstanding Young Scientists of Shandong Province (Grant No. BS2013DX008).

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant numbers 61573220, 61473134, 61304045]; Scientific Research Foundation for Outstanding Young Scientists of Shandong Province [grant number BS2013DX008].

Notes on contributors

Wei Wang

Wei Wang received his PhD degree in control science and engineering from Shenzhen Graduate School, Harbin Institute of Technology, in 2010. He is currently an associate professor at Shandong University, Jinan Shandong, China. His research interests include optimal control and estimation for delayed systems, distributed control and estimation.

Fangfang Zhang

Fangfang Zhang received his PhD degree in control theory and control engineering from Shandong University in 2015. Currently, he is a lecturer in the School of Electrical Engineering, Zhengzhou University, Zhengzhou, China. His research interests include distributed control and distributed optimization.

Chunyan Han

Chunyan Han received her PhD degree in control theory and control engineering from Shandong University in 2010. She is currently an associate professor at the School of Electrical Engineering, University of Jinan. Her research interest covers optimal control and estimation, time-delay systems, and Markov jump linear systems.