Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-26T11:46:20.538Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamic logarithmic state and control quantization for continuous-time linear systems

Published online by Cambridge University Press:  07 January 2022

Jiashuo Wang ,
Shuo Pan  and
Zhiyu Xi Open the ORCID record for Zhiyu Xi [Opens in a new window]
Jiashuo Wang
Affiliation:
Rail Transit Technology Institute of CRSC (Beijing) Industry Group Co., Ltd., Beihang, China
Shuo Pan
Affiliation:
School of Automation Science and Electrical Engineering, Beihang University, Beijing, China
Zhiyu Xi*
Affiliation:
School of Automation Science and Electrical Engineering, Beihang University, Beijing, China
*
*Corresponding author. E-mail: z.xi@buaa.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper addresses logarithmic quantizers with dynamic sensitivity design for continuous-time linear systems with a quantized feedback control law. The dynamics of state quantization and control quantization sensitivities during “zoom-in”/“zoom-out” stages are proposed. Dwell times of the dynamic sensitivities are co-designed. It is shown that with the proposed algorithm, a single-input continuous-time linear system can be stabilized by quantized feedback control via adopting sensitivity varying algorithm under certain assumptions. Also, the advantage of logarithmic quantization is sustained while achieving stability. Simulation results are provided to verify the theoretical analysis.

Keywords

logarithmic quantizersaturationfeedback stabilizationlinear systemsdynamic sensitivity
Type
Research Article
Information
Robotica , Volume 40 , Issue 7 , July 2022 , pp. 2215 - 2230
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Gupta, R. A. and Chow, M.-Y., “Networked control systems overview and research trends,” IEEE Trans. Ind. Electron. 57(07), 2527–2535 (2010).CrossRefGoogle Scholar
Siuhi, S. and Mwakalonge, J., “Opportunities and challenges of smart mobile applications in transportation,” J. Traffic Transp. Eng. (English Edition) 16(03), 582–592 (2016).CrossRefGoogle Scholar
Cooper, D. E., “Intelligent transportation systems for smart cities: A progress review,” Sci. China (Inf. Sci.) 55(12), 2908–2914 (2012).Google Scholar
Alioto, M. and Shahghasemi, M., “The internet of things on its edge: Trends toward its tipping point,” IEEE Consum. Electron. Mag. 7(01), 77–87 (2018).CrossRefGoogle Scholar
Sarigiannidis, P., Karapistoli, E. and Economides, A. A., “Modeling the internet of things under attack: A G-network approach,” IEEE Internet Things J. 4(06), 1964–1977 (2017).Google Scholar
Theodorou, T. and Mamatas, L., “Software Defined Topology Control Strategies for the Internet of Things,” IEEE Conference on Network Function Virtualization and Software Defined Networks (2017) pp. 236–241.Google Scholar
Azuma, S.-i. and Sugie, T. , “Optimal dynamic quantizers for discrete-valued input control,” Automatica 44, 396–406 (2008).CrossRefGoogle Scholar
Elia, N. and Mitter, S. K., “Stabilization of linear systems with limited information,” IEEE Trans. Autom. Control 46(09), 1384–1400 (2011).Google Scholar
Delchamps, D. F., “Stabilizing a linear system with quantized state feedback,” IEEE Trans. Autom. Control 35(08), 916–924 (1990).Google Scholar
Wang, S., Wang, Z., Dong, H. and Chen, Y., “Distributed state estimation under random parameters and dynamic quantizations over sensor networks: A dynamic event-based approach,” IEEE Trans. Inf, Signal. Process. Networks 6, 732–743 (2020).Google Scholar
Zhou, T., Zuo, Z. and Wang, Y., “Self-triggered and event-triggered control for linear systems with quantization,” IEEE Trans. Syst. Man Cybern. Syst. 50(9), 3136–3144 (2020).CrossRefGoogle Scholar
Fu, M. and Xie, L., “The sector bound approach to quantized feedback control,” IEEE Trans. Autom. Control 50(11), 1698–1711 (2005).Google Scholar
Brockett, R. W. and Liberzon, D., “Quantized feedback stabilization of linear systems,” IEEE Trans. Autom. Control 45(07), 1279–1289 (2000).Google Scholar
Wang, H., Bai, W. and Liu, P. X., “Finite-time adaptive fault-tolerant control for nonlinear systems with multiple faults,” IEEE/CAA J. Automatica Sinica 6(6), 1417–1427 (2019).CrossRefGoogle Scholar
Chen, M., Wang, H. and Liu, X., “Adaptive fuzzy practical fixed-time tracking control of nonlinear systems,” IEEE Trans. Fuzzy Syst. 29(3), 664–673 (2021).CrossRefGoogle Scholar
Li, M., Sun, J. and Dou, L., “Stability of an improved dynamic quantized system with time varying delay and packet loss,” IET Control Theory Appl. 9(6), 988–995 (2015).CrossRefGoogle Scholar
Sheng, L., Wang, Z., Wang, W. and Alsaadi, F. E., “Output-feedback control for nonlinear stochastic systems with successive packet dropouts and uniform quantization effects,” IEEE Trans. Syst. Man Cybern. 47(7), 1181–1191 (2016).Google Scholar
Liu, K., Fridman, E. and Johansson, K. H., “Dynamic quantization of uncertain linear networked control systems,” Automatica 59, 248–255 (2015).CrossRefGoogle Scholar
Su, L. and Chesi, G., “Robust stability of uncertain linear systems with input and output quantization and packet loss,” Automatica 87, 267–273 (2018).CrossRefGoogle Scholar
Wang, D., Wang, J. and Wang, W., “ $H_\infty$ Controller design of networked control systems with Markov packet packet Dropouts,” IEEE Trans. Syst. Man Cybern. 43(3), 689–697 (2013).CrossRefGoogle Scholar