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Soft Computing

, Volume 22, Issue 8, pp 2705–2715 | Cite as

Decentralized adaptive optimal stabilization of nonlinear systems with matched interconnections

  • Chaoxu Mu
  • Changyin Sun
  • Ding Wang
  • Aiguo Song
  • Chengshan Qian
Methodologies and Application

Abstract

In this paper, we investigate the decentralized feedback stabilization and adaptive dynamic programming (ADP)-based optimization for the class of nonlinear systems with matched interconnections. The decentralized control law of the overall system is designed by integrating all controllers of the isolated subsystems, and it satisfies the optimality on the basis of optimal control laws of all the subsystems. For solving the optimal control problems of these isolated subsystems, the policy iteration algorithm is used to approximately solve the Hamilton–Jacobi–Bellman equations in the framework of ADP with the neural network implementation, where a set of critic neural networks is constructed to estimate the optimal cost functions, and the approximate optimal control laws can be obtained after the learning of critic neural networks. The weight estimation errors of the critic networks and the stability of all isolated subsystems are proved based on the Lyapunov theory. Finally, the performance of the proposed decentralized optimal control strategy is verified by simulation results.

Keywords

Adaptive dynamic programming (ADP) Interconnected nonlinear systems Neural networks Decentralized control Matched interconnections 

Notes

Acknowledgements

This work was supported by National Natural Science Foundation of China under Grants 61304018, 61304086, 61533017, 61533008, 61520106009, and U1501251, China Postdoctoral Science Foundation under Grant 2014M561559, Tianjin Natural Science Foundation under Grant 14JCQNJC05400, Beijing Natural Science Foundation under Grant 4162065, Tianjin Key Laboratory of Process Measurement and Control under Grant TKLPMC-201612, and the Early Career Development Award of SKLMCCS.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Human and animals rights

This paper does not contain any studies with human participants or animals performed by any of the authors.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Chaoxu Mu
    • 1
    • 2
  • Changyin Sun
    • 1
  • Ding Wang
    • 3
  • Aiguo Song
    • 4
  • Chengshan Qian
    • 5
  1. 1.School of AutomationSoutheast UniversityNanjingChina
  2. 2.Tianjin Key Laboratory of Process Measurement and Control, School of Electrical and Information EngineeringTianjin UniversityTianjinChina
  3. 3.The State Key Laboratory of Management and Control for Complex Systems, Institute of AutomationChinese Academy of SciencesBeijingChina
  4. 4.School of Instrument Science and EngineeringSoutheast UniversityNanjingChina
  5. 5.School of Computer and SoftwareNanjing University of Information Science and TechnologyNanjingChina

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