Abstract
In this paper, we investigate an \(\boldsymbol{\epsilon }\)-Nash Equilibrium seeking problem subject to external disturbance. The game is played by multi-agent with two order integrators under full information. In order to estimate and remedy external disturbance, a static extended stubborn state observer is proposed. An \(\boldsymbol{\epsilon }\)-Nash Equilibrium seeking strategy is proposed to regulate the action of each agent to around Nash Equilibrium points regard to full information. Finally, a numerical example is presented to verify the validity of the proposed \(\boldsymbol{\epsilon }\)-Nash equilibrium seeking method.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Semsar-Kazerooni, E., Khorasani, K.: Multi-agent team cooperation: a game theory approach. Automatica 45(10), 2205–2213 (2009)
Karavas, C.-S., Arvanitis, K., Papadakis, G.: A game theory approach to multi-agent decentralized energy management of autonomous polygeneration microgrids. Energies 10(11), 1756 (2017)
Pendharkar, P.C.: Game theoretical applications for multi-agent systems. Expert Syst. Appl. 39(1), 273–279 (2012)
Wang, C., et al.: Consensus disturbance rejection for Lipschitz nonlinear multi-agent systems with input delay: a DOBC approach. J. Frankl. Inst. 354(1), 298–315 (2017)
Natori, K., Ohnishi, K.: A design method of communication disturbance observer for time-delay compensation, taking the dynamic property of network disturbance into account. IEEE Trans. Ind. Electron. 55(5), 2152–2168 (2008)
Bae, J., Zhang, W., Tomizuka, M.: Compensation of packet loss for a network-based rehabilitation system. In: 2012 IEEE International Conference on Robotics and Automation. IEEE (2012)
Li, S., et al.: Disturbance Observer-Based Control: Methods and Applications. CRC Press (2014)
Han, J.: From PID to active disturbance rejection control. IEEE Trans. Ind. Electron. 56(3), 900–906 (2009)
Chen, W.-H., et al.: A nonlinear disturbance observer for robotic manipulators. IEEE Trans. Ind. Electron. 47(4), 932–938 (2000)
Han, J.: A class of extended state observers for uncertain systems. Control. Decis. 10(1), 85–88 (1995)
Guo, B.-Z., Zhao, Z.: On the convergence of an extended state observer for nonlinear systems with uncertainty. Syst. Control. Lett. 60(6), 420–430 (2011)
Zhao, Z.-L., Guo, B.-Z.: Extended state observer for uncertain lower triangular nonlinear systems. Syst. Control. Lett. 85, 100–108 (2015)
Alessandri, A., Zaccarian, L.: Stubborn state observers for linear time-invariant systems. Automatica 88, 1–9 (2018)
Talole, S.E., Kolhe, J.P., Phadke, S.B.: Extended-state-observer-based control of flexible-joint system with experimental validation. IEEE Trans. Ind. Electron. 57(4), 1411–1419 (2009)
Yao, J., Jiao, Z., Ma, D.: Adaptive robust control of DC motors with extended state observer. IEEE Trans. Ind. Electron. 61(7), 3630–3637 (2013)
Liu, J., et al.: Extended state observer-based sliding-mode control for three-phase power converters. IEEE Trans. Ind. Electron. 64(1), 22–31 (2016)
Flåm, S.D.: Equilibrium, evolutionary stability and gradient dynamics. Int. Game Theory Rev. 4(04), 357–370 (2002)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Chunhe, M., Peng, Z., Yuan, Y. (2022). \(\boldsymbol{\epsilon }\)-Nash Equilibrium Seeking for Two Order Multi-agent with Disturbance Rejection. In: Yan, L., Duan, H., Yu, X. (eds) Advances in Guidance, Navigation and Control . Lecture Notes in Electrical Engineering, vol 644. Springer, Singapore. https://doi.org/10.1007/978-981-15-8155-7_278
Download citation
DOI: https://doi.org/10.1007/978-981-15-8155-7_278
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-8154-0
Online ISBN: 978-981-15-8155-7
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)