Skip to main content
SpringerLink
Log in

Decentralized Control of Continuous-Time Interconnected Nonlinear Systems

  • Chapter
  • First Online:
Adaptive Dynamic Programming with Applications in Optimal Control

Part of the book series: Advances in Industrial Control ((AIC))

  • 3890 Accesses

Abstract

In this chapter, by using neural network (NN)-based online learning optimal control approach, a decentralized control strategy is developed to stabilize a class of continuous-time large-scale interconnected nonlinear systems . It is proven that the decentralized control strategy of the overall system can be established by adding appropriate feedback gains to the optimal control laws of the isolated subsystems . Then, an online policy iteration (PI) algorithm is developed to solve the Hamilton–Jacobi–Bellman equations related to the optimal control problem. By constructing a set of critic NNs, the cost functions can be obtained by NN approximation, followed by the control laws. Furthermore, as a generalization, an NN-based decentralized control law is developed to stabilize the large-scale interconnected nonlinear systems using an online model-free integral PI algorithm. The model-free PI approach can solve the decentralized control problem for large-scale interconnected nonlinear systems with unknown dynamics. Finally, two simulation examples are provided to illustrate the effectiveness of the present decentralized control scheme.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Abu-Khalaf M, Lewis FL (2005) Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach. Automatica 41(5):779–791

    Article  MathSciNet  MATH  Google Scholar 

  2. Bakule L (2008) Decentralized control: an overview. Ann Rev Control 32(1):87–98

    Article  MathSciNet  Google Scholar 

  3. Beard RW, Saridis GN, Wen JT (1997) Galerkin approximations of the generalized Hamilton–Jacobi–Bellman equation. Automatica 33(12):2159–2177

    Article  MathSciNet  MATH  Google Scholar 

  4. Glad ST (1984) On the gain margin of nonlinear and optimal regulators. IEEE Trans Autom Control AC–29(7):615–620

    Article  MathSciNet  MATH  Google Scholar 

  5. Jiang Y, Jiang ZP (2012) Computational adaptive optimal control for continuous-time linear systems with completely unknown dynamics. Automatica 48(10):2699–2704

    Article  MathSciNet  MATH  Google Scholar 

  6. Jiang Y, Jiang ZP (2012) Robust adaptive dynamic programming for large-scale systems with an application to multimachine power systems. IEEE Trans Circ Syst II Express Briefs 59(10):693–697

    Google Scholar 

  7. Khan SG, Herrmann G, Lewis FL, Pipe T, Melhuish C (2012) Reinforcement learning and optimal adaptive control: an overview and implementation examples. Ann Rev Contorl 36(1):42–59

    Article  Google Scholar 

  8. Lee JY, Park JB, Choi YH (2012) Integral Q-learning and explorized policy iteration for adaptive optimal control of continuous-time linear systems. Automatica 48(11):2850–2859

    Article  MathSciNet  MATH  Google Scholar 

  9. Lewis FL, Liu D (2012) Reinforcement learning and approximate dynamic programming for feedback control. Wiley, Hoboken

    Book  Google Scholar 

  10. Lewis FL, Vrabie D (2009) Reinforcement learning and adaptive dynamic programming for feedback control. IEEE Circ Syst Mag 9(3):32–50

    Article  MathSciNet  Google Scholar 

  11. Liang J, Venayagamoorthy GK, Harley RG (2012) Wide-area measurement based dynamic stochastic optimal power flow control for smart grids with high variability and uncertainty. IEEE Trans Smart Grid 3(1):59–69

    Article  Google Scholar 

  12. Liu D, Wang D, Zhao D, Wei Q, Jin N (2012) Neural-network-based optimal control for a class of unknown discrete-time nonlinear systems using globalized dual heuristic programming. IEEE Trans Autom Sci Eng 9(3):628–634

    Article  Google Scholar 

  13. Liu D, Wang D, Li H (2014) Decentralized stabilization for a class of continuous-time nonlinear interconnected systems using online learning optimal control approach. IEEE Trans Neural Network Learn Syst 25(2):418–428

    Article  MathSciNet  Google Scholar 

  14. Liu D, Li C, Li H, Wang D, Ma H (2015) Neural-network-based decentralized control of continuous-time nonlinear interconnected sytems with unknown dynamics. Neurocomputing 165:90–98

    Article  Google Scholar 

  15. Mehraeen S, Jagannathan S (2011) Decentralized optimal control of a class of interconnected nonlinear discrete-time systems by using online Hamilton-Jacobi-Bellman formulation. IEEE Trans Neural Network 22(11):1757–1769

    Article  Google Scholar 

  16. Park JW, Harley RG, Venayagamoorthy GK (2005) Decentralized optimal neuro-controllers for generation and transmission devices in an electric power network. Eng Appl Artif Intell 18(1):37–46

    Article  Google Scholar 

  17. Rudin W (1976) Principles of mathematical analysis. McGraw-Hill, New York

    MATH  Google Scholar 

  18. Saberi A (1988) On optimality of decentralized control for a class of nonlinear interconnected systems. Automatica 24(1):101–104

    Article  MathSciNet  MATH  Google Scholar 

  19. Siljak DD (1991) Decentralized control of complex systems. Academic Press, Boston

    MATH  Google Scholar 

  20. Siljak DD, Zecevic AI (2005) Control of large-scale systems: beyond decentralized feedback. Ann Rev Control 29(2):169–179

    Article  MATH  Google Scholar 

  21. Sutton RS, Barto AG (1998) Reinforcement learning: an introduction. MIT Press, Cambridge

    Google Scholar 

  22. Tsitsiklis JN, Athans M (1984) Guaranteed robustness properties of multivariable nonlinear stochastic optimal regulators. IEEE Trans Autom Control AC–29(8):690–696

    Article  MathSciNet  MATH  Google Scholar 

  23. Vamvoudakis KG, Lewis FL (2010) Online actor-critic algorithm to solve the continuous-time infinite horizon optimal control problem. Automatica 46(5):878–888

    Article  MathSciNet  MATH  Google Scholar 

  24. Vrabie D, Lewis FL (2009) Neural network approach to continuous-time direct adaptive optimal control for partially unknown nonlinear systems. Neural Network 22(3):237–246

    Article  MATH  Google Scholar 

  25. Wang FY, Zhang H, Liu D (2009) Adaptive dynamic programming: an introduction. IEEE Comput Intell Mag 4(2):39–47

    Article  Google Scholar 

  26. Wang D, Liu D, Li H, Ma H (2014) Neural-network-based robust optimal control design for a class of uncertain nonlinear systems via adaptive dynamic programming. Inf Sci 282:167–179

    Article  MathSciNet  Google Scholar 

  27. Werbos PJ (1977) Advanced forecasting methods for global crisis warning and models of intelligence. General Syst Yearb 22:25–38

    Google Scholar 

  28. Werbos PJ (1992) Approximate dynamic programming for real-time control and neural modeling. In: White DA, Sofge DA (eds) Handbook of intelligent control: neural, fuzzy, and adaptive approaches (Chapter 13). Van Nostrand Reinhold, New York

    Google Scholar 

  29. Zhang H, Liu D, Luo Y, Wang D (2013) Adaptive dynamic programming for control: algorithms and stability. Springer, London

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Automation, Chinese Academy of Sciences, Beijing, China

    Derong Liu, Qinglai Wei & Ding Wang

  2. Tianjin University, Tianjin, China

    Xiong Yang

  3. Tencent Inc., Shenzhen, China

    Hongliang Li

Authors
  1. Derong Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qinglai Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ding Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xiong Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Hongliang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Derong Liu .

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Cite this chapter

Liu, D., Wei, Q., Wang, D., Yang, X., Li, H. (2017). Decentralized Control of Continuous-Time Interconnected Nonlinear Systems. In: Adaptive Dynamic Programming with Applications in Optimal Control. Advances in Industrial Control. Springer, Cham. https://doi.org/10.1007/978-3-319-50815-3_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-50815-3_10

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-50813-9

  • Online ISBN: 978-3-319-50815-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation