Skip to main content
SpringerLink
Log in

Optimal Error Dynamics in Missile Guidance

  • Chapter
  • First Online:
Optimal Guidance and Its Applications in Missiles and UAVs

Part of the book series: Springer Aerospace Technology ((SAT))

Abstract

This chapter investigates the optimal convergence pattern of the tracking error that frequently appears in missile guidance problems and proposes an optimal error dynamics for guidance law design to achieve various operational objectives. The proposed optimal error dynamics is derived by solving a linear quadratic optimal control problem through Schwarz’s inequality approach. The properties of the proposed optimal error dynamics are discussed. The significant contribution of the proposed result lies in that it can provide a link between existing nonlinear guidance laws and optimal guidance laws for missile systems. Therefore, the advantages of both techniques can be fully exploited by using the proposed approach: existing nonlinear guidance laws can be converted to their optimal forms and the physical meaning of them can then be easily explained. Four illustration examples, including zero zero-effort-miss (ZEM) guidance, impact angle guidance, impact time control, impact angle control as well as impact angle and impact time control, are provided to show how the proposed results can be applied to missile guidance law design. The performance of the new guidance laws is demonstrated by numerical simulation.

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 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
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. Shima T, Idan M, Golan OM (2006) Sliding-mode control for integrated missile autopilot guidance. J Guid Control Dyn 29(2):250–260

    Article  Google Scholar 

  2. Idan M, Shima T, Golan OM (2007) Integrated sliding mode autopilot-guidance for dual-control missiles. J Guid Control Dyn 30(4):1081–1089

    Article  Google Scholar 

  3. Dwivedi P, Bhale P, Bhattacharyya A, Padhi R (2016) Generalized estimation and predictive guidance for evasive targets. IEEE Trans Aerosp Electron Syst 52(5):2111–2122

    Article  Google Scholar 

  4. He S, Lee C-H (2018) Gravity-turn-assisted optimal guidance law. J Guid Control Dyn 41(1):171–183

    Article  Google Scholar 

  5. Kim M, Grider KV (1973) Terminal guidance for impact attitude angle constrained flight trajectories. IEEE Trans Aerosp Electron Syst AES–9(6):852–859

    Article  Google Scholar 

  6. Kim BS, Lee JG, Han HS (1998) Biased png law for impact with angular constraint. IEEE Trans Aerosp Electr Syst 34(1):277–288

    Article  Google Scholar 

  7. Lu P, Doman DB, Schierman JD (2006) Adaptive terminal guidance for hypervelocity impact in specified direction. J Guid Control Dyn 29(2):269–278

    Article  Google Scholar 

  8. Erer KS, Merttopçuoglu O (2012) Indirect impact-angle-control against stationary targets using biased pure proportional navigation. J Guid Control Dyn 35(2):700–704

    Article  Google Scholar 

  9. Lee C-H, Kim T-H, Tahk M-J (2013) Interception angle control guidance using proportional navigation with error feedback. J Guid Control Dyn 36(5):1556–1561

    Article  Google Scholar 

  10. Kumar SR, Rao S, Ghose D (2012) Sliding-mode guidance and control for all-aspect interceptors with terminal angle constraints. J Guid Control Dyn 35(4):1230–1246

    Article  Google Scholar 

  11. Kumar SR, Rao S, Ghose D (2014) Nonsingular terminal sliding mode guidance with impact angle constraints. J Guid Control Dyn 37(4):1114–1130

    Article  Google Scholar 

  12. He S, Song T, Lin D (2017) Impact angle constrained integrated guidance and control for maneuvering target interception. J Guid Control Dyn 40(10):2653–2661

    Article  Google Scholar 

  13. Jeon I-S, Lee J-I, Tahk M-J (2006) Impact-time-control guidance law for anti-ship missiles. IEEE Trans Control Syst Technol 14(2):260–266

    Article  Google Scholar 

  14. Jeon I-S, Lee J-I, Tahk M-J (2010) Homing guidance law for cooperative attack of multiple missiles. J Guid Control Dyn 33(1):275–280

    Article  Google Scholar 

  15. Kim T-H, Lee C-H, Tahk M-J, Jeon I-S (2013) Biased png law for impact-time control. Trans Jpn Soc Aeronaut Space Sci 56(4):205–214

    Article  Google Scholar 

  16. Cho N, Kim Y (2016) Modified pure proportional navigation guidance law for impact time control. J Guid Control Dyn 39(4):852–872

    Article  Google Scholar 

  17. Harl N, Balakrishnan SN (2012) Impact time and angle guidance with sliding mode control. IEEE Trans Control Syst Technol 20(6):1436–1449

    Article  Google Scholar 

  18. Moon J, Kim K, Kim Y (2001) Design of missile guidance law via variable structure control. J Guid Control Dyn 24(4):659–664

    Article  MathSciNet  Google Scholar 

  19. Brierley SD, Longchamp R (1990) Application of sliding-mode control to air-air interception problem. IEEE Trans Aerosp Electron Syst 26(2):306–325

    Article  Google Scholar 

  20. Koren A, Idan M, Golan OM et al (2008) Integrated sliding mode guidance and control for a missile with on-off actuators. J Guid Control Dyn 31(1):204

    Article  Google Scholar 

  21. Yang C-D, Chen H-Y (1998) Nonlinear \(h_\infty \) robust guidance law for homing missiles. J Guid Control Dyn 21:882–890

    Article  Google Scholar 

  22. Lechevin N, Rabbath CA (2004) Lyapunov-based nonlinear missile guidance. J Guid Control Dyn 27(6):1096–1102

    Article  Google Scholar 

  23. Talole SE, Banavar RN (1998) Proportional navigation through predictive control. J Guid Control Dyn 21:1004–1005

    Article  Google Scholar 

  24. Menon PK, Sweriduk GD, Ohlmeyer EJ (2003) Optimal fixed-interval integrated guidance-control laws for hit-to-kill missiles. In: AIAA guidance, navigation, and control conference, Austin, Texas. AIAA

    Google Scholar 

  25. Weiss G, Rusnak I (2015) All-aspect three-dimensional guidance law based on feedback linearization. J Guid Control Dyn 38(12):2421–2428

    Article  Google Scholar 

  26. Zarchan P (2012) Tactical and strategic missile guidance. American Institute of Aeronautics and Astronautics

    Google Scholar 

  27. He S, Wang W, Lin D, Lei H (2018) Consensus-based two-stage salvo attack guidance. IEEE Trans Aerosp Electron Syst 54(3):1555–1566

    Article  Google Scholar 

  28. Chen X, Wang J (2017) Nonsingular sliding-mode control for field-of-view constrained impact time guidance. J Guid Control Dyn 41(5):1214–1222

    Article  Google Scholar 

  29. He S, Kim M, Song T, Lin D (2018) Three-dimensional salvo attack guidance considering communication delay. Aerosp Sci Technol 73:1–9

    Article  Google Scholar 

  30. Lee C-H, Seo M-G (2018) New insights into guidance laws with terminal angle constraints. J Guid Control Dyn 41(8):1832–1837

    Article  Google Scholar 

  31. Ryoo C-K, Cho H, Tahk M-J (2005) Optimal guidance laws with terminal impact angle constraint. J Guid Control Dyn 28(4):724–732

    Article  Google Scholar 

  32. Ryoo C-K, Cho H, Tahk M-J (2006) Time-to-go weighted optimal guidance with impact angle constraints. IEEE Trans Control Syst Technol 14(3):483–492

    Article  Google Scholar 

  33. Ohlmeyer EJ, Phillips CA (2006) Generalized vector explicit guidance. J Guid Control Dyn 29(2):261–268

    Article  Google Scholar 

  34. Lee C-H, Kim T-H, Tahk M-J, Whang I-H (2013) Polynomial guidance laws considering terminal impact angle and acceleration constraints. IEEE Trans Aerosp Electron Syst 49(1):74–92

    Article  Google Scholar 

  35. Tahk M-J, Shim S-W, Hong S-M, Lee C-H, Choi H-L (2018) Impact time control based on time-to-go prediction for sea-skimming anti-ship missiles. IEEE Trans Aerosp Electron Syst 54(4):2043–2052

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Aerospace Engineering, Beijing Institute of Technology, Beijing, China

    Shaoming He

  2. Department of Aerospace Engineering, Korea Advanced Institute of Science and Technology, Daejeon, Korea (Republic of)

    Chang-Hun Lee

  3. Aerospace, Transport and Manufacturing, Cranfield University, Cranfield, UK

    Hyo-Sang Shin & Antonios Tsourdos

Authors
  1. Shaoming He
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chang-Hun Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hyo-Sang Shin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Antonios Tsourdos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shaoming He .

Rights and permissions

Reprints and permissions

Copyright information

© 2020 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

He, S., Lee, CH., Shin, HS., Tsourdos, A. (2020). Optimal Error Dynamics in Missile Guidance. In: Optimal Guidance and Its Applications in Missiles and UAVs. Springer Aerospace Technology. Springer, Cham. https://doi.org/10.1007/978-3-030-47348-8_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-47348-8_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-47347-1

  • Online ISBN: 978-3-030-47348-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation