Event-Triggered Control of Port-Hamiltonian Systems Under Time-Delay Communication

Authors

Ernesto Aranda-Escolástico, Leonardo J. Colombo, María Guinaldo, Antonio Visioli

Abstract

We study the problem of periodic event-triggered control of interconnected port-Hamiltonian systems subject to time-varying delays in their communication. In particular, we design a threshold parameter for the event-triggering condition, a sampling period, and a maximum allowable delay such that interconnected port-Hamiltonian control systems with periodic event-triggering mechanism under a time-delayed communication are able to achieve asymptotically stable behaviour. Simulation results are presented to validate the theory.

Citation

• Journal: IEEE Control Systems Letters
• Year: 2024
• Volume: 8
• Issue:
• Pages: 175–180
• Publisher: Institute of Electrical and Electronics Engineers (IEEE)
• DOI: 10.1109/lcsys.2024.3355811

BibTeX

@article{Aranda_Escol_stico_2024,
  title={{Event-Triggered Control of Port-Hamiltonian Systems Under Time-Delay Communication}},
  volume={8},
  ISSN={2475-1456},
  DOI={10.1109/lcsys.2024.3355811},
  journal={IEEE Control Systems Letters},
  publisher={Institute of Electrical and Electronics Engineers (IEEE)},
  author={Aranda-Escolástico, Ernesto and Colombo, Leonardo J. and Guinaldo, María and Visioli, Antonio},
  year={2024},
  pages={175--180}
}

Download the bib file

References

• Schaft, A. L2-Gain and Passivity Techniques in Nonlinear Control. Lecture Notes in Control and Information Sciences (Springer Berlin Heidelberg, 1996). doi:10.1007/3-540-76074-1 – 10.1007/3-540-76074-1
• van der Schaft, A. & Jeltsema, D. Port-Hamiltonian Systems Theory: An Introductory Overview. Foundations and Trends® in Systems and Control vol. 1 173–378 (2014) – 10.1561/2600000002
• Sprangers, O., Babuska, R., Nageshrao, S. P. & Lopes, G. A. D. Reinforcement Learning for Port-Hamiltonian Systems. IEEE Transactions on Cybernetics vol. 45 1017–1027 (2015) – 10.1109/tcyb.2014.2343194
• Reyes-Báez, R., van der Schaft, A. & Jayawardhana, B. Virtual contractivity-based control of fully-actuated mechanical systems in the port-Hamiltonian framework. Automatica vol. 141 110275 (2022) – 10.1016/j.automatica.2022.110275
• Yuksel, B., Secchi, C., Bulthoff, H. H. & Franchi, A. Reshaping the physical properties of a quadrotor through IDA-PBC and its application to aerial physical interaction. 2014 IEEE International Conference on Robotics and Automation (ICRA) 6258–6265 (2014) doi:10.1109/icra.2014.6907782 – 10.1109/icra.2014.6907782
• Aoues, S., Cardoso-Ribeiro, F. L., Matignon, D. & Alazard, D. Modeling and Control of a Rotating Flexible Spacecraft: A Port-Hamiltonian Approach. IEEE Transactions on Control Systems Technology vol. 27 355–362 (2019) – 10.1109/tcst.2017.2771244
• Schiffer, J., Fridman, E., Ortega, R. & Raisch, J. Stability of a class of delayed port-Hamiltonian systems with application to microgrids with distributed rotational and electronic generation. Automatica vol. 74 71–79 (2016) – 10.1016/j.automatica.2016.07.022
• Cervera, J., van der Schaft, A. J. & Baños, A. Interconnection of port-Hamiltonian systems and composition of Dirac structures. Automatica vol. 43 212–225 (2007) – 10.1016/j.automatica.2006.08.014
• Ortega, R., van der Schaft, A., Castanos, F. & Astolfi, A. Control by Interconnection and Standard Passivity-Based Control of Port-Hamiltonian Systems. IEEE Transactions on Automatic Control vol. 53 2527–2542 (2008) – 10.1109/tac.2008.2006930
• Castaños, F., Ortega, R., van der Schaft, A. & Astolfi, A. Asymptotic stabilization via control by interconnection of port-Hamiltonian systems. Automatica vol. 45 1611–1618 (2009) – 10.1016/j.automatica.2009.03.015
• Hespanha, J. P., Naghshtabrizi, P. & Xu, Y. A Survey of Recent Results in Networked Control Systems. Proceedings of the IEEE vol. 95 138–162 (2007) – 10.1109/jproc.2006.887288
• Gupta, R. A. & Mo-Yuen Chow. Networked Control System: Overview and Research Trends. IEEE Transactions on Industrial Electronics vol. 57 2527–2535 (2010) – 10.1109/tie.2009.2035462
• Pasumarthy, R. & Kao, C.-Y. On stability of time delay Hamiltonian systems. 2009 American Control Conference 4909–4914 (2009) doi:10.1109/acc.2009.5160619 – 10.1109/acc.2009.5160619
• Aoues, S., Lombardi, W., Eberard, D. & Seuret, A. Robust stability for delayed port-Hamiltonian systems using improved Wirtinger-based inequality. 53rd IEEE Conference on Decision and Control 3119–3124 (2014) doi:10.1109/cdc.2014.7039870 – 10.1109/cdc.2014.7039870
• Schiffer, J., Fridman, E. & Ortega, R. Stability of a class of delayed port-Hamiltonian systems with application to droop-controlled microgrids. 2015 54th IEEE Conference on Decision and Control (CDC) 6391–6396 (2015) doi:10.1109/cdc.2015.7403226 – 10.1109/cdc.2015.7403226
• Sun, W. & Fu, B. Adaptive control of time‐varying uncertain non‐linear systems with input delay: a Hamiltonian approach. IET Control Theory & Applications vol. 10 1844–1858 (2016) – 10.1049/iet-cta.2015.1165
• Cai, L.-C. Simultaneous stabilization of Port-Hamiltonian systems subject to actuation saturation and input delay. International Journal of Automation and Computing vol. 18 849–854 (2015) – 10.1007/s11633-015-0928-4
• Farid, Y. & Ruggiero, F. Finite-time extended state observer and fractional-order sliding mode controller for impulsive hybrid port-Hamiltonian systems with input delay and actuators saturation: Application to ball-juggler robots. Mechanism and Machine Theory vol. 167 104577 (2022) – 10.1016/j.mechmachtheory.2021.104577
• Tabuada, P. Event-Triggered Real-Time Scheduling of Stabilizing Control Tasks. IEEE Transactions on Automatic Control vol. 52 1680–1685 (2007) – 10.1109/tac.2007.904277
• Heemels, W. P. M. H., Johansson, K. H. & Tabuada, P. An introduction to event-triggered and self-triggered control. 2012 IEEE 51st IEEE Conference on Decision and Control (CDC) 3270–3285 (2012) doi:10.1109/cdc.2012.6425820 – 10.1109/cdc.2012.6425820
• Aranda-Escolastico, E. et al. Event-Based Control: A Bibliometric Analysis of Twenty Years of Research. IEEE Access vol. 8 47188–47208 (2020) – 10.1109/access.2020.2978174
• Hu, S. & Yue, D. Event-triggered control design of linear networked systems with quantizations. ISA Transactions vol. 51 153–162 (2012) – 10.1016/j.isatra.2011.09.002
• Heemels, W. P. M. H., Donkers, M. C. F. & Teel, A. R. Periodic Event-Triggered Control for Linear Systems. IEEE Transactions on Automatic Control vol. 58 847–861 (2013) – 10.1109/tac.2012.2220443
• Yue, D., Tian, E. & Han, Q.-L. A Delay System Method for Designing Event-Triggered Controllers of Networked Control Systems. IEEE Transactions on Automatic Control vol. 58 475–481 (2013) – 10.1109/tac.2012.2206694
• Aranda-Escolástico, E., Guinaldo, M., Gordillo, F. & Dormido, S. A novel approach to periodic event-triggered control: Design and application to the inverted pendulum. ISA Transactions vol. 65 327–338 (2016) – 10.1016/j.isatra.2016.08.019
• Aranda-Escolástico, E., Colombo, L. J. & Guinaldo, M. Periodic event-triggered targeted shape control of Lagrangian systems with discrete-time delays. ISA Transactions vol. 117 139–149 (2021) – 10.1016/j.isatra.2021.01.048
• Aranda-Escolástico, E., Rodríguez, C., Guinaldo, M., Luis Guzmán, J. & Dormido, S. Asynchronous periodic event-triggered control with dynamical controllers. Journal of the Franklin Institute vol. 355 3455–3469 (2018) – 10.1016/j.jfranklin.2018.01.037
• Fridman, E. Tutorial on Lyapunov-based methods for time-delay systems. European Journal of Control vol. 20 271–283 (2014) – 10.1016/j.ejcon.2014.10.001
• Seuret, A. & Gouaisbaut, F. Wirtinger-based integral inequality: Application to time-delay systems. Automatica vol. 49 2860–2866 (2013) – 10.1016/j.automatica.2013.05.030
• Nonlinear control theory. AccessScience McGraw-Hill Professional https://doi.org/10.1036/1097-8542.455500 – 10.1036/1097-8542.455500
• Angeli, D., Sontag, E. D. & Wang, Y. A characterization of integral input-to-state stability. IEEE Transactions on Automatic Control vol. 45 1082–1097 (2000) – 10.1109/9.863594