On stability and convergence of suboptimal estimation for systems over lossy networks without acknowledgement

Abstract

This paper concentrates on the suboptimal state estimation problem for systems without acknowledgement (ACK). The ACK signal is used for informing the estimator of whether control-input packets have been lost during the transmission or not. For such systems, which are usually regarded as NACK systems, the optimal estimator has been proved to be beset by exponentially increasing computational burden so that it is scarcely possible to be implemented in practice and then the suboptimal estimation becomes a necessary need. Inspired by the idea of multiple-model approaches, we first design an efficient suboptimal estimator for NACK systems to significantly improve computational efficiency. More importantly, we obtained a sufficient and necessary condition to characterise the stability of this proposed suboptimal estimator, which depends only on the packet loss rate (PLR) of the observation regardless of the control-input PLR. We also prove that its estimation error will converge to that of the optimal estimator under a certain condition. A distinguishing feature of the suboptimal estimator proposed in this paper is that not only its stability and convergence can be determined theoretically, but also they are proved to be the same as those of the optimal one for NACK systems.

Keywords:

• State estimation
• suboptimal estimator
• stability
• convergence
• lossy networks

Disclosure statement

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

Additional information

Funding

This work was supported by the National Key Research and Development Program of China [grant number 2019YFB1312600] and the National Natural Science Foundation of China [grant numbers 52075480, 51935009].

Notes on contributors

Zhenyu Liu

Zhenyu Liu received the B.S. and Ph.D. in Mechanical Engineering, Zhejiang University, Hangzhou, China, in 1996 and 2002, respectively. He is currently a Professor of Mechanical Engineering and State Key Laboratory of CAD&CG, Zhejiang University, Hangzhou, China. His current research interests include digital twin, intelligent design, machine vision and robotics.

Shi Liang

Shi Liang received the B.S. degree from Nanjing University of Aeronauticsand Astronautics, Nanjing, China, in 2013.He is currently working toward the Ph.D. degree in Zhejiang University, China. His research interests include filtering and its applications for networked systems and CPS.

Chan Qiu

Chan Qiu is a lecturer at the School of Mechanical Engineering and State Key Laboratory of CAD & CG, Zhejiang University, China. He received his PhD from Zhejiang University, China, in 2012. He is currently working on digital design and manufacturing of complex products.

Xiang Peng

Xiang Peng is a lecturer at the College of Mechanical Engineering and Key Laboratory of E&M, Zhejiang University of Technology, China. He received his PhD from Zhejiang University, China, in 2014. He is currently working on product digital design and simulation.

Jianrong Tan

Jianrong Tan is an academician of China Engineering Academy, and is currently a professor and Ph.D. candidate supervisor at School of Mechanical Engineering, Zhejiang University, China. He received the M.S. from Huazhong University of Science and Technology, Wuhan, China in 1987 and the Ph.D. from Zhejiang University in 1992. His main research interests include virtual prototyping, enterprise informatization, CAX and robotics.