Abstract
This paper is concerned with the integrated design of event-triggered control and mobile non-collocated sensor and actuator networks for a diffusion process. Firstly, an estimator is designed to estimate the states of the diffusion process and the mobile strategies of the sensors are given. Then, event-triggered control strategies are presented aiming at the benefit of saving the limited network resources. Based on the event-triggering mechanism, the value of estimation states will be sent to the controllers and the mobile actuators will move to the designated positions within the respective spatial domain. Thirdly, by using the Lyapunov functional approach, sufficient conditions are established to guarantee the boundedness of the event-triggered control system. Moreover, the existence of the lower bound of minimum inter-event time is also proved to exclude the Zeno behavior. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed results.
Similar content being viewed by others
References
I. F. Akyildiz and I. H. Kasimoglu, “Wireless sensor and actor networks: Research challenges,” AdHoc Networks, vol. 2, no. 4, pp. 351–367, 2004.
D. Satoh, K. Kobayashi, and Y. Yamashita, “MPC-based co-design of control and routing for wireless sensor and actuator networks,” International Journal of Control, Automation, and Systems, vol. 16, no. 3, pp. 953–960, 2018.
M. A. Demetriou, “Guidance of mobile actuator-plus-sensor networks for improved control and estimation of distributed parameter systems,” IEEE Transactions on Automatic Control, vol. 55, no. 7, pp. 1570–1584, 2010.
M. A. Demetriou and I. I. Hussein, “Estimation of spatially distributed processes using mobile spatially distributed sensor network,” SIAM Journal on Control and Optimization, vol. 48, no. 1, pp. 266–291, 2009.
H. N. Wu and X. W. Zhang, “Static output feedback stabilization for a linear parabolic PDE system with time-varying delay via mobile collocated actuator/sensor pairs,” Automatica, vol. 117, Article ID:108993, 2020.
Z. P. Wang, H. N. Wu, and X. H. Wang, “Sampled-data control for linear time-delay distributed parameter systems,” ISA Transactions, vol. 92, pp. 75–83, 2019.
X. W. Yin, X. N. Song, and M. Wang, “Passive fuzzy control design for a class of nonlinear distributed parameter systems with time-varying delay,” International Journal of Control, Automation, and Systems, vol. 18, no. 4, pp. 911–921, 2020.
H. H. Ji, B. T. Cui, and X. Z. Liu, “Adaptive control of markov jump distributed parameter systems via model reference,” Fuzzy Sets and Systems, vol. 392, pp. 115–135, 2020.
T. D. Nguyen, “Boundary output feedback of second-order distributed parameter systems,” Systems and Control Letters, vol. 58, no. 7, pp. 519–528, 2009.
Z. J. Zhao, Z. J. Liu, W. He, K. S. Hong, and H. X. Li, “Boundary adaptive fault-tolerant control for a flexible Timoshenko arm with backlash-like hysteresis,” Automatica, vol. 130, Article ID:109690, 2021.
A. Selivanov and E. Fridman, “Delayed H∞ control of 2D diffusion systems under delayed pointlike measurements,” Automatica, vol. 109, Article ID:108541, 2019.
A. Khapalov, “Mobile point controls versus locally distributed ones for the controllability of the semilinear parabolic equation,” SIAM Journal on Control & Optimization, vol. 40, no. 1, pp. 231–252, 2001.
Y. Q. Chen, Z. M. Wang, and J. S. Liang, “Actuation scheduling in mobile actuator networks for spatial-temporal feedback control of a diffusion process with dynamic obstacle avoidance,” Proc. of IEEE International Conference on Mechatronics and Automation, pp. 752–757, 2005.
C. Tricaud, M. Patan, D. Ucinski, and Y. Q. Chen, “D-optimal trajectory design of heterogeneous mobile sensors for parameter estimation of distributed systems,” Proc. of American Control Conference, pp. 663–668, 2008.
M. A. Demetriou, “Design of consensus and adaptive consensus filters for distributed parameter systems,” Automatica, vol. 46, no. 2, pp. 300–311, 2010.
M. A. Demetriou, “Adaptive control of 2-D PDEs using mobile collocated actuator/sensor pairs with augmented vehicle dynamics,” IEEE Transactions on Automatic Control, vol. 57, no. 12, pp. 2979–2993, 2012.
H. Y. Chao, Y. Q. Chen, and W. Ren, “Consensus of information in distributed control of a diffusion process using centroidal Voronoi tessellation,” Proc. of the 46th IEEE Conference on Decision and Control, pp. 1441–1446, 2007.
Z. X. Jiang, B. T. Cui, X. Y. Lou, and B. Zhuang, “Improved control of distributed parameter systems using wireless sensor and actuator networks: An observer-based method,” Chinese Physics B, vol. 26, no. 4, Article ID:040200, 2017.
Z. X. Jiang, B. T. Cui, and X. Y. Lou, “Distributed consensus estimation for diffusion systems with missing measurements over sensor networks,” International Journal of Systems Science, vol. 47, no. 12, pp. 2753–2761, 2016.
M. A. Demetriou, “Incorporating communication delays in the guidance of a moving actuator/sensor for performance enhancement of controlled distributed parameter systems,” Proc. of American Control Conference, pp. 826–831, 2009.
X. N. Song, M. Wang, S. Song, and Z. Wang, “Quantized output feedback control for nonlinear Markovian jump distributed parameter systems with unreliable communication links,” Applied Mathematics and Computation, vol. 353, pp. 371–395, 2019.
Z. Y. Yao and N. H. El-Farra, “Resource-aware model predictive control of spatially distributed processes using event-triggered communication,” Proc. of IEEE 52nd Annual Conference on Decision and Control (CDC), pp. 3726–3731, 2013.
T. T. Hu, Z. He, X. J. Zhang, and S. M. Zhong, “Leader-following consensus of fractional-order multi-agent systems based on event-triggered control,” Nonlinear Dynamics, vol. 99, no. 3, pp. 2219–2232, 2020.
K. P. Zhang, T. Zhao, and S. Y. Dian, “Dynamic output feedback control for nonlinear networked control systems with a two-terminal event-triggered mechanism,” Nonlinear Dynamics, vol. 100, no. 1, pp. 2537–2555, 2020.
X. M. Tang, M. Y. Li, S. B. Wei, and B. C. Ding, “Event-triggered synchronous distributed model predictive control for multi-agent systems,” International Journal of Control, Automation, and Systems, vol. 19, no. 3, pp. 1273–1282, 2021.
W. Y. Mu, B. T. Cui, X. Y. Lou, and W. Li, “Optimal switching policy for performance enhancement of distributed parameter systems based on event-driven control,” Chinese Physics B, vol. 23, no. 7, Article ID:070204, 2014.
W. Y. Mu, F. Qiu, B. Zhuang, and L. G. Chen, “Optimal actuator switching synthesis of observer-based event-triggered state feedback control for distributed parameter systems,” Journal of the Franklin Institute, vol. 358, no. 1, pp. 384–399, 2021.
A. Selivanov and E. Fridman, “Distributed event-triggered control of diffusion semilinear PDEs,” Automatica, vol. 68, pp. 344–351, 2016.
H. H. Ji, H. Zhang, and B. T. Cui, “Event-triggered H∞ filtering control for a class of distributed parameter systems with Markovian switching topology,” Journal of the Franklin Institute, vol. 355, no. 13, pp. 5928–5956, 2018.
R. Curtain and H. Zwart, Introduction to Infinite-Dimensional Systems Theory: A State-Space Approach, Springer, New York, U.S.A., 2020.
Author information
Authors and Affiliations
Corresponding author
Additional information
This work is partially supported by National Natural Science Foundation of China (61807016), Jiangsu Provincial Natural Science Foundation of China (BK20201340) and China Postdoctoral Science Foundation (2018M642160).
Zhengxian Jiang received her Ph.D. degree in control theory and control engineering from Jiangnan University, China, in 2016. Her research interests include distributed parameter systems and multi-agent systems.
Bo Zhuang received his Ph.D. degree in control science and engineering from Jiangnan University, China, in 2019. His research interests include control of distributed parameter systems, boundary control of fractional-order PDEs, and multi-agent systems.
Xuyang Lou received his Ph.D. degree in control theory and control engineering from Jiangnan University, China, in 2009. His research interests include optimization and control of networked electromechanical systems, and analysis and control of hybrid systems.
Wei Wu received his Ph.D. degree in control science and engineering from University of Kaiserslautern, Germany, in 2014. His research interests include nonlinear control systems, networked and event-triggered control systems, and control of aerial system.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Jiang, Z., Zhuang, B., Lou, X. et al. Integrated Design of Event-triggered Control and Mobile Non-collocated SANs for a Diffusion Process. Int. J. Control Autom. Syst. 20, 2915–2926 (2022). https://doi.org/10.1007/s12555-021-0200-3
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12555-021-0200-3