Simultaneous exponential stabilization for stochastic port-controlled Hamiltonian systems with actuator saturations, fading channels and delays

Authors

Yaping Tang, Weiwei Sun, Dongqing Liu

Abstract

This paper is concerned with the simultaneous exponential stabilization problem for a set of stochastic port-controlled Hamiltonian (PCH) systems. Due to the limited bandwidth of the channels, the phenomena of fading channels and transmission delays which are described by a time-varying stochastic model always occur in the communication channels from the controller to the actuator. Meanwhile, actuator saturation constraint is taken into account. On the basis of dissipative Hamiltonian structural and saturating actuator properties, those stochastic PCH systems are combined to generate an augmented system. By utilizing the stochastic analysis theory, sufficient criterions are given for the simultaneous stabilization controller design ensuring that the closed-loop system is simultaneously exponentially mean-square stable (SEMSS). For the case that there exist external disturbances in the systems, some results on stability analysis and controller design are given. The developed controller design scheme is proved by a three-helicopter model simulation example.

Citation

• Journal: Journal of the Franklin Institute
• Year: 2022
• Volume: 359
• Issue: 3
• Pages: 1130–1151
• Publisher: Elsevier BV
• DOI: 10.1016/j.jfranklin.2021.12.014

BibTeX

@article{Tang_2022,
  title={{Simultaneous exponential stabilization for stochastic port-controlled Hamiltonian systems with actuator saturations, fading channels and delays}},
  volume={359},
  ISSN={0016-0032},
  DOI={10.1016/j.jfranklin.2021.12.014},
  number={3},
  journal={Journal of the Franklin Institute},
  publisher={Elsevier BV},
  author={Tang, Yaping and Sun, Weiwei and Liu, Dongqing},
  year={2022},
  pages={1130--1151}
}

Download the bib file

References

• Hua Deng & Krstic, M. Output-feedback stochastic nonlinear stabilization. IEEE Trans. Automat. Contr. 44, 328–333 (1999) – 10.1109/9.746260
• Ding, Y., Cheng, J., Liu, H. & Zhong, S. Local input-to-state stabilization of time-delay systems subject to actuator saturation and external disturbance. Journal of the Franklin Institute 357, 4154–4170 (2020) – 10.1016/j.jfranklin.2020.01.020
• Elia, N. Remote stabilization over fading channels. Systems & Control Letters 54, 237–249 (2005) – 10.1016/j.sysconle.2004.08.009
• Eustace, R. W., Woodyatt, B. A., Merrington, G. L. & Runacres, A. Fault Signatures Obtained From Fault Implant Tests on an F404 Engine. Journal of Engineering for Gas Turbines and Power 116, 178–183 (1994) – 10.1115/1.2906789
• Fang, Z. & Gao, C. Stabilization of Input-Disturbed Stochastic Port-Hamiltonian Systems Via Passivity. IEEE Trans. Automat. Contr. 62, 4159–4166 (2017) – 10.1109/tac.2017.2676619
• Fu, B., Li, S., Wang, X. & Guo, L. Output feedback based simultaneous stabilization of two Port-controlled Hamiltonian systems with disturbances. Journal of the Franklin Institute 356, 8154–8166 (2019) – 10.1016/j.jfranklin.2019.02.039
• Gündeş, A. N. Simultaneous stabilization of MIMO systems with integral action controllers. Automatica 44, 1156–1160 (2008) – 10.1016/j.automatica.2007.08.003
• Haddad, W. M., Rajpurohit, T. & Jin, X. Energy-based feedback control for stochastic port-controlled Hamiltonian systems. Automatica 97, 134–142 (2018) – 10.1016/j.automatica.2018.07.031
• Kohan-sedgh, P., Khayatian, A. & Behmanesh-Fard, N. Simultaneous stabilization of polynomial nonlinear systems via density functions. Journal of the Franklin Institute 357, 1690–1706 (2020) – 10.1016/j.jfranklin.2019.11.033
• Li, X., Song, S. & Wu, J. Exponential Stability of Nonlinear Systems With Delayed Impulses and Applications. IEEE Trans. Automat. Contr. 64, 4024–4034 (2019) – 10.1109/tac.2019.2905271
• Li, X. & Yang, X. Lyapunov stability analysis for nonlinear systems with state-dependent state delay. Automatica 112, 108674 (2020) – 10.1016/j.automatica.2019.108674
• Li, Y. & Lin, Z. An asymmetric Lyapunov function for linear systems with asymmetric actuator saturation. Intl J Robust & Nonlinear 28, 1624–1640 (2017) – 10.1002/rnc.3976
• Lin, Z. Global Control of Linear Systems with Saturating Actuators. Automatica 34, 897–905 (1998) – 10.1016/s0005-1098(98)00023-5
• Liu, Q., Chen, W., Wang, Z. & Qiu, L. Stabilization of MIMO Systems Over Multiple Independent and Memoryless Fading Noisy Channels. IEEE Trans. Automat. Contr. 64, 1581–1594 (2019) – 10.1109/tac.2018.2854643
• Liu, Y., Wang, Z., Dong, H. & Liu, H. Anti-disturbance filter design for a class of stochastic systems with fading channels. Sci. China Inf. Sci. 63, (2020) – 10.1007/s11432-019-9903-2
• Mao, (2007)
• Maschke, Port-controlled Hamiltonian systems: modeling origins and system theoretic properties. (1992)
• Nageshrao, S. P., Lopes, G. A. D., Jeltsema, D. & Babuska, R. Port-Hamiltonian Systems in Adaptive and Learning Control: A Survey. IEEE Trans. Automat. Contr. 61, 1223–1238 (2016) – 10.1109/tac.2015.2458491
• Ortega, R., van der Schaft, A., Maschke, B. & Escobar, G. Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica 38, 585–596 (2002) – 10.1016/s0005-1098(01)00278-3
• Ren, Y., Zhu, P., Zhao, Z., Yang, J. & Zou, T. Adaptive Fault-Tolerant Boundary Control for a Flexible String With Unknown Dead Zone and Actuator Fault. IEEE Trans. Cybern. 52, 7084–7093 (2022) – 10.1109/tcyb.2020.3044144
• Ren, Y., Zhao, Z., Zhang, C., Yang, Q. & Hong, K.-S. Adaptive Neural-Network Boundary Control for a Flexible Manipulator With Input Constraints and Model Uncertainties. IEEE Trans. Cybern. 51, 4796–4807 (2021) – 10.1109/tcyb.2020.3021069
• Satoh, S. & Saeki, M. Bounded stabilisation of stochastic port-Hamiltonian systems. International Journal of Control 87, 1573–1582 (2014) – 10.1080/00207179.2014.880127
• 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 74, 71–79 (2016) – 10.1016/j.automatica.2016.07.022
• Shen, Adaptive L2 disturbance attenuation of Hamiltonian systems with parametric perturbation and application to power systems. (2000)
• Shen, Y., Wang, Z., Shen, B. & Alsaadi, F. E. Event-based recursive filtering for a class of nonlinear stochastic parameter systems over fading channels. International Journal of General Systems 47, 401–415 (2018) – 10.1080/03081079.2018.1457031
• Sun, Simultaneous stabilization of a class of nonlinear descriptor systems via Hamiltonian function method. Sci. China Ser. F (2009)
• Sun, Stabilization analysis of time-delay Hamiltoniansystems in the presence of saturation. Appl. Math. Comput. (2011)
• Sun, W., Liu, D. & Tang, Y. Global asymptotic stabilisation andH∞control for a class of nonlinear Hamiltonian singular systems with delays and saturation. International Journal of Systems Science 51, 811–825 (2020) – 10.1080/00207721.2020.1740823
• Sun, W., Lv, X. & Qiu, M. Distributed Estimation for Stochastic Hamiltonian Systems With Fading Wireless Channels. IEEE Trans. Cybern. 52, 4897–4906 (2022) – 10.1109/tcyb.2020.3023547
• Tan, C., Zhang, H. & Wong, W. S. Delay-Dependent Algebraic Riccati Equation to Stabilization of Networked Control Systems: Continuous-Time Case. IEEE Trans. Cybern. 48, 2783–2794 (2018) – 10.1109/tcyb.2017.2750221
• Tang, Y., Sun, W., Liu, D. & Li, X. Finite-Time Simultaneous Stabilization for Stochastic Port-Controlled Hamiltonian Systems over Delayed and Fading Channels. Complexity 2020, 1–12 (2020) – 10.1155/2020/6387025
• Touron, M., Dieulot, J.-Y., Gomand, J. & Barre, P.-J. A port-Hamiltonian framework for operator force assisting systems: Application to the design of helicopter flight controls. Aerospace Science and Technology 72, 493–501 (2018) – 10.1016/j.ast.2017.11.035
• Wang, Y., Feng, G. & Cheng, D. Simultaneous stabilization of a set of nonlinear port-controlled Hamiltonian systems. Automatica 43, 403–415 (2007) – 10.1016/j.automatica.2006.09.008
• Wang, Y., Li, C. & Cheng, D. Generalized Hamiltonian realization of time-invariant nonlinear systems. Automatica 39, 1437–1443 (2003) – 10.1016/s0005-1098(03)00132-8
• Zidong Wang, Yao Wang & Yurong Liu. Global Synchronization for Discrete-Time Stochastic Complex Networks With Randomly Occurred Nonlinearities and Mixed Time Delays. IEEE Trans. Neural Netw. 21, 11–25 (2010) – 10.1109/tnn.2009.2033599
• Wei, A. & Wang, Y. Stabilization and H∞ control of nonlinear port-controlled Hamiltonian systems subject to actuator saturation. Automatica 46, 2008–2013 (2010) – 10.1016/j.automatica.2010.08.001
• Wu, J.-L. Simultaneous stabilization for a collection of single-input nonlinear systems. IEEE Trans. Automat. Contr. 50, 328–337 (2005) – 10.1109/tac.2005.843877
• XU, B. Stability robustness bounds for linear systems with multiple time-varying delayed perturbations. International Journal of Systems Science 28, 1311–1317 (1997) – 10.1080/00207729708929486
• Yang, F., Wang, Z., Hung, Y. S. & Gani, M. <tex>$H_infty$</tex>Control for Networked Systems With Random Communication Delays. IEEE Trans. Automat. Contr. 51, 511–518 (2006) – 10.1109/tac.2005.864207
• Zhang, S., Wang, Z., Ding, D. & Shu, H. H∞ output-feedback control with randomly occurring distributed delays and nonlinearities subject to sensor saturations and channel fadings. Journal of the Franklin Institute 351, 4124–4141 (2014) – 10.1016/j.jfranklin.2014.04.011
• Zhou, Simultaneous stabilization of marine dynamic positioning system based on PCH model. (2014)