Skip to main content

Decentralized Inverse Optimal Control for Trajectory Tracking

  • Chapter
  • First Online:
Decentralized Neural Control: Application to Robotics

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 96))

  • 671 Accesses

Abstract

This chapter proposes a decentralized control for trajectory tracking of a nonlinear system using a neural inverse optimal control approach in order to design a suitable controller for each subsystem. Accordingly, each subsystem is approximated by an identifier using a discrete-time recurrent high order neural network (RHONN), trained with an extended Kalman filter (EKF) algorithm. The neural identifier scheme is used to model the uncertain nonlinear system, and based on this neural model and the knowledge of a control Lyapunov function, then an inverse optimal controller is synthesized in order to achieve trajectory tracking. Applicability of the proposed approach is illustrated via real-time control of a Shrimp robot.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 99.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 129.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 129.99
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. Al-Tamimi, A., Lewis, F.L., Abu-Khalaf, M.: Discrete-time nonlinear HJB solution using approximate dynamic programming: convergence proof. IEEE Trans. Syst. Man Cybern. Part B Cybern. 38(4), 943–949 (2008)

    Article  Google Scholar 

  2. Basar, T., Olsder, G.J.: Dynamic Noncooperative Game Theory. Academic Press, New York (1995)

    MATH  Google Scholar 

  3. Davila, J., Fridman, L., Levant, A.: Second-Order sliding mode observer for mechanical systems. IEEE Trans. Autom. Control 50(11), 1785–1789 (2005)

    Article  MathSciNet  Google Scholar 

  4. Davila, J., Fridman, L., Poznyak, A.: Observation and identification of mechanical systems via second order sliding modes. Int. J. Control 79(10), 1251–1262 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  5. Haddad, W.M., Chellaboina, V.-S., Fausz, J.L., Abdallah, C.: Identification and control of dynamical systems using neural networks. J. Frankl. Inst. 335(5), 827–839 (1998)

    Article  MATH  Google Scholar 

  6. Kirk, D.E.: Optimal Control Theory: An Introduction. Dover Publications Inc, Englewood Cliffs (2004)

    Google Scholar 

  7. Lewis, F.L., Syrmos, V.L.: Optimal Control. Wiley, New York (1995)

    Google Scholar 

  8. Ohsawa, T., Bloch, A.M., Leok, M.: Discrete Hamilton-Jacobi theory and discrete optimal control. In: Proceedings of the 49th IEEE Conference on Decision and Control, pp. 5438–5443. Atlanta (2010)

    Google Scholar 

  9. Sanchez, E.N., Ornelas-Tellez, F.: Discrete-time inverse optimal control for nonlinear systems. CRC Press, Boca Raton (2013)

    MATH  Google Scholar 

  10. Sepulchre, R., Jankovic, M., Kokotovic, P.V.: Constructive Nonlinear Control. Springer, London (1997)

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ramon Garcia-Hernandez .

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Garcia-Hernandez, R., Lopez-Franco, M., Sanchez, E.N., Alanis, A.Y., Ruz-Hernandez, J.A. (2017). Decentralized Inverse Optimal Control for Trajectory Tracking. In: Decentralized Neural Control: Application to Robotics. Studies in Systems, Decision and Control, vol 96. Springer, Cham. https://doi.org/10.1007/978-3-319-53312-4_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-53312-4_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-53311-7

  • Online ISBN: 978-3-319-53312-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics