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Authors
Kothari, Mangal; Padhi, Radhakant

Digital Object Identifier (DOI)
10.3182/20070625-5-FR-2916.00111

Page Numbers:
651-656

Index Terms
model predictive control,model predictive static programming,MPSP,energy-insensitive guidance,explicit guidance,ballistic missile guidance

Abstract
Combining the newly developed nonlinear model predictive static programming technique with null range direction concept, a novel explicit energy-insensitive guidance design method is presented in this paper for long range flight vehicles, which leads to a closed form solution of the necessary guidance command update. Owing to the closed form nature, it does not lead to computational difficulties and the proposed optimal guidance algorithm can be implemented online. The guidance law is verified in a solid motor propelled long range flight vehicle, for which coming up with an effective guidance law is more difficult as compared to a liquid engine propelled vehicle (mainly because of the absence of thrust cutoff facility). Assuming the starting point of the second stage to be a deterministic point beyond the atmosphere, the scheme guides the vehicle properly so that it completes the mission within a tight error bound. The simulation results demonstrate its ability to intercept the target, even with an uncertainty of greater than 10% in burnout time.

References

[1] Bryson, A. E. and Y. C. Ho (1975). Applied Optimal
    Control. Hemisphere Publishing Corporation.
[2] Battin, R. H. (1982). Guidance Evolution - A Personal
    Narrative. Journal of Guidance, Control and Dynamics.
     Vol. 5. pp. 97-110.
[3] Zarchan, P (1997). Tactical and Strategic Missile
    Guidance. Proceeding in Astronautics and Aeronautics,
     AIAA Tactical Missile Series. Vol. 176.
    pp. 97-110.
[4] Padhi, R. (1999). An Optimal Explicit Guidance
    Scheme for Ballistic Missile with Solid Motors.
    Proceedings of AIAA Guidance, Navigation, and
    Control Conference. AIAA-4140.
[5] Wheelon, A. D. (1959). Free Flight of a Ballistic
    Missile. ARS journal. 915-926.
[6] Greensite, A. L. (1970). Analysis and Design of Space
    Vehicle Flight Control System. Spartan Bok.
[7] White, J. E. (1993). Cut-off Insensitive Guidance With
    Variable Time of Flight. Proceedings of AIAA
    Guidance, Navigation, and Control Conference.
    AIAA 3785. pp. 793-800.
[8] Padhi, R. and M. Kothari (in Press). A Closed Form
    Nonlinear Explicit Guidance Scheme for Long
    Range Flight Vehicles. Proceedings of National
    System Conference, Indian Institute of Technology,
     Bombay.
[9] Padhi, R., M. Kothari and A. Kamath. Model Predictive
     Static Programming: A Promising Real-time
    Technique for Optimal Control Design. Technical
    Report: IISc/AE/LINCGODS/RP/2006/01.