Abstract
The development of a homing missile guidance law against an intelligent adversary requires the solution to a differential game. First, we formulate the deterministic homing guidance problem as a linear dynamic system with an indefinite quadratic performance criterion (LQ). This formulation allows the navigation ratio to be greater than three, which is obtained by the one-sided linear-quadratic regulator and appears to be more realistic. However, this formulation does not allow for saturation in the actuators. A deterministic game allowing saturation is formulated and shown to be superior to the LQ guidance law, even though there is no control penalty. To improve the performance of the quadratic differential game solution in the presence of saturation, trajectory-shaping feature is added. Finally, if there are uncertainties in the measurements and process noise, a disturbance attenuation function is formulated that is converted into a differential game. Since only the terminal state enters the cost criterion, the resulting estimator is a Kalman filter, but the guidance gains are a function of the assumed system variances.
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References
Basar T, Bernhard P (1995) H∞ optimal control and related minimax design problems: a dynamic game approach, 1st edn. Birkhäuser, Boston
Ben-Asher JZ, Yaesh I (1998) Advances in missile guidance theory, vol 180. Progress in astronautics and aeronautics. AIAA, Washington, DC
Ben-Asher JZ, Shinar Y, Wiess H, Levinson S (2004) Trajectory shaping in linear-quadratic pursuit-evasion games. AIAA J. Guidance, Control and Dynamics 27(6):1102–1105
Bryson AE, Ho YC (1975) Applied optimal control. Hemisphere, New York
Gutman S (1979) On optimal guidance for homing missiles. AIAA J. Guidance, Control and Dynamics 3(4):296–300
Nesline WN, Zarchan P (1981) A new look at classical vs. modern homing missile guidance. AIAA J. Guidance, Control and Dynamics 4(1):878–880
Rhee I, Speyer JL (1991) Game theoretic approach to a finite-time disturbance attenuation problem. IEEE Trans Autom Control 36(9):1021–1032
Shinar J (1981) In: Leondes CT (ed) Automatic control systems, vol 17, 8th edn. Academic Press, New York
Shinar J (1989) On new concepts effecting guidance law synthesis of future interceptor missiles. In: AIAA CP 89-3589, guidance, navigation and control conference, Boston. AIAA
Speyer JL (1976) An adaptive terminal guidance scheme based on an exponential cost criterion with application to homing missile guidance. IEEE Trans Autom Control 48:371–375
Speyer JL, Chung WH (2008) Stochastic processes, estimation, and control, 1st edn. SIAM, Philadelphia
Speyer JL, Jacobson DH (2010) Primer on optimal control theory, 1st edn. SIAM, Philadelphia
Zarchan P (1997) Tactical and strategic missile guidance, progress in astronautics and aeronautics. AIAA, Washington, DC
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We thank Dr. Maya Dobrovinsky from Elbit Systems for converting part of this document from Word to LATE X.
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Ben-Asher, J.Z., Speyer, J.L. (2018). Games in Aerospace: Homing Missile Guidance. In: Başar, T., Zaccour, G. (eds) Handbook of Dynamic Game Theory. Springer, Cham. https://doi.org/10.1007/978-3-319-44374-4_25
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DOI: https://doi.org/10.1007/978-3-319-44374-4_25
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