Game Theoretic Regular Perturbation Guidance Strategies for Aeroassisted Plane Change Missions

  • Marc R. Ilgen
  • Jason L. Speyer


The calculus of variations regular perturbation methodology is extended to solve a class of differential game problems and to apply this methodology to the development of robust approximate optimal guidance laws for aeroassisted plane change missions. The class of differential game problems examined arises from the treatment of system parameter uncertainties as deterministic control variables controlled by Nature as an intelligent adversary. When the parameter uncertainties are introduced using the concept of fictitious feedback loops, the optimal solutions to the resulting formulation are sought from the class of solutions satisfying first and second order necessary conditions for a game theoretic saddle point. The solution to the zeroth order problem (the problem resulting from setting a small parameter a to zero in the equations of motion) is found analytically while first and higher order corrections are found from a set of numerical quadratures. The required calculations are quite modest in number and can easily be performed in real time. Impressive numerical results indicate the robust behavior of this guidance law.


  1. 1.
    M. R. Ilgen and J. L. Speyer, “Robust Approximate Optimal Plane Change Guidance Using Differential Game Theoretic Methods,” AIAA Paper 92–4453-CP, AIAA Guidance, Navigation and Control Conference Hilton Head, South Carolina, August 10–12, 1992.Google Scholar
  2. 2.
    CP, M. R. Ilgen, J. L. Speyer and C. T. Leondes, “Robust Approximate Optimal Guidance Strategies for Aeroassisted Plane Change Missions: A Game Theoretic Approach,” in Control and Dynamic Systems (C. T. Leondes, ed.), Vol. 52, 1992.Google Scholar

Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Marc R. Ilgen
    • 1
  • Jason L. Speyer
    • 2
  1. 1.The Aerospace Corporation El SegundoUSA
  2. 2.School of Engineering and Applied ScienceUniversity of CaliforniaLos AngelesUSA

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