Advertisement

Decentralized Stabilization for Nonlinear Systems with Unknown Mismatched Interconnections

  • Bo ZhaoEmail author
  • Ding Wang
  • Guang Shi
  • Derong Liu
  • Yuanchun Li
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9949)

Abstract

This paper establishes a neural network and policy iteration based decentralized control scheme to stabilize large-scale nonlinear systems with unknown mismatched interconnections. For relaxing the common assumption of upper boundedness on interconnections when designing the decentralized optimal control, interconnections are approximated by neural networks with local signals of isolated subsystem and replaced reference signals of coupled subsystems. By using the adaptive estimation term, the performance index function is constructed to reflect the replacement error. Hereafter, it is proven that the developed decentralized optimal control policies can guarantee the closed-loop large-scale nonlinear system to be uniformly ultimately bounded. The effectiveness of the developed scheme is verified by a simulation example.

Keywords

Adaptive Dynamic Programming Decentralized control Unknown mismatched interconnections Policy iteration 

Notes

Acknowledgments

This work was supported in part by the National Natural Science Foundation of China under Grants 61233001, 61273140, 61304086, 61374105, 61374051, 61533017, 61603387 and U1501251, in part by the Scientific and Technological Development Plan Project in Jilin Province of China under Grants 20150520112JH and 20160414033GH, and in part by Beijing Natural Science Foundation under Grant 4162065.

References

  1. 1.
    Vrabie, D., Pastravanu, O., Abu-Khalaf, M., et al.: Adaptive optimal control for continuous-time linear systems based on policy iteration. Automatica 45(2), 477–484 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Wang, D., Liu, D., Wei, Q., et al.: Optimal control of unknown nonaffine nonlinear discrete-time systems based on adaptive dynamic programming. Automatica 48(8), 1825–1832 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Jiang, Y., Jiang, Z.: Robust adaptive dynamic programming for large-scale systems with an application to multimachine power systems. IEEE Trans. Circ. II 59(10), 693–697 (2012)Google Scholar
  4. 4.
    Wei, Q., Liu, D.: Adaptive dynamic programming for optimal tracking control of unknown nonlinear systems with application to coal gasification. IEEE Trans. Autom. Sci. Eng. 11(4), 1020–1036 (2014)CrossRefGoogle Scholar
  5. 5.
    Zhang, H., Luo, Y., Liu, D.: Neural-network-based near-optimal control for a class of discrete-time affine nonlinear systems with control constraints. IEEE Trans. Neural Netw. 20(9), 1490–1503 (2009)CrossRefGoogle Scholar
  6. 6.
    Liu, D., Wang, D., Li, H.: Decentralized stabilization for a class of continuous-time nonlinear interconnected systems using online learning optimal control approach. IEEE Trans. Neural Netw. Learn. Syst. 25(2), 418–428 (2014)CrossRefGoogle Scholar
  7. 7.
    Bian, T., Jiang, Y., Jiang, Z.: Decentralized adaptive optimal control of large-scale systems with application to power systems. IEEE Trans. Ind. Electron. 62(4), 2439–2447 (2015)CrossRefGoogle Scholar
  8. 8.
    Liu, D., Li, C., Li, H., et al.: Neural-network-based decentralized control of continuous-time nonlinear interconnected systems with unknown dynamics. Neurocomputing 165, 90–98 (2015)CrossRefGoogle Scholar
  9. 9.
    Lu, C., Si, J., Xie, X.: Direct heuristic dynamic programming for damping oscillations in a large power system. IEEE Trans. Syst. Man Cybern. Part B Cybern. 38(4), 1008–1013 (2008)CrossRefGoogle Scholar
  10. 10.
    Molina, D., Venayagamoorthy, G., Liang, J., et al.: Intelligent local area signals based damping of power system oscillations using virtual generators and approximate dynamic programming. IEEE Trans. Smart Grid. 4(1), 498–508 (2013)CrossRefGoogle Scholar
  11. 11.
    Bernstein, D., Amato, C., Hansen, E., et al.: Policy iteration for decentralized control of Markov decision processes. J. Artif. Intell. Res. 34(1), 89–132 (2009)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Chen, W., Li, J.: Decentralized output-feedback neural control for systems with unknown interconnections. IEEE Trans. Syst. Man Cybern. Part B Cybern. 38(1), 258–266 (2008)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Bo Zhao
    • 1
    Email author
  • Ding Wang
    • 1
  • Guang Shi
    • 1
  • Derong Liu
    • 2
  • Yuanchun Li
    • 3
  1. 1.The State Key Laboratory of Management and Control for Complex SystemsInstitute of Automation, Chinese Academy of SciencesBeijingChina
  2. 2.School of Automation and Electrical EngineeringUniversity of Science and Technology BeijingBeijingChina
  3. 3.Department of Control Science and EngineeringChangchun University of TechnologyChangchunChina

Personalised recommendations