Abstract
A new guidance law is proposed for interceptor missiles by using a differential game formulation with bounded controls. The interceptor is steered by the aerodynamic-lift control system and the divert-thrusters control system. By using game space decomposition, the parameter effects of divert-thrusters control system on homing performance are investigated. Under propellant limits and given the time constant of the divert-thrusters control system, the hit-to-kill performance requires the following conditions. Firstly, the maximum acceleration generated by the divert-thrusters control system is greater than a critical value. Secondly, the thrusters close after interception terminates. Thirdly, the operation time of the divert-thrusters control system is sufficient long to cancel the miss distance. These results are also demonstrated by a realistic ballistic missile-defense simulation program.
Similar content being viewed by others
References
Shinar, J., Shima, T.: Nonorthodox guidance law development approach for intercepting maneuvering targets. J. Guid. Control Dyn. 25, 658–666 (2002)
Hirokawa, R., Satot, K., Manabe, S.: Autopilot design for a missile with reaction-jet using coefficient diagram method. In: AIAA Guidance, Navigation, and Control Conf., pp. 1–8. AIAA, Montreal (2001)
Bryson, A.E., Ho, Y.C.: Applied Optimal Control, pp. 154–155. Blasdell Publishing Company, Waltham (1969)
Garber, V.: Optimal intercept laws for accelerating targets. AIAA J. 6, 2196–2198 (1968)
Cottrell, R.G.: Optimal intercept guidance for short-range tactical missiles. AIAA J. 9, 1414–1415 (1971)
Shima, T., Shinar, J.: Time-varying linear pursuit–evasion game models with bounded controls. J. Guid. Control Dyn. 25, 425–432 (2002)
Shinar, J., Shima, T., Kebke, A.: On the validity of linearized analysis in the interception of reentry vehicles. In: Proc. AIAA Guidance, Navigation, and Control Conf., pp. 1050–1060. AIAA, Reston (1998)
Gutman, S., Leitmann, G.: Optimal strategies in the neighborhood of a collision course. AIAA J. 14, 1210–1212 (1976)
Gutman, S.: On optimal guidance for homing missiles. J. Guid. Control Dyn. 3, 296–300 (1979)
Shinar, J. (ed.) Solution Techniques for Realistic Pursuit-Evasion Games. Advances in Control and Dynamic Systems, pp. 63–124. Academic Press, New York (1981)
Belapolsky, O., Ben-Asher, Z.J.: On two formulations of linear quadratic optimal guidance. In: AIAA Guidance, Navigation, and Control Conference and Exhibit. AIAA, Hilton Head (2007)
Turetsky, V.: Upper bounds of the pursuer control based on a linear-quadratic differential game. J. Optim. Theory Appl. 121, 163–191 (2004)
Turetsky, V., Shinar, J.: Missile guidance laws bases on pursuit-evasion game formulations. Automatica 39, 607–618 (2003)
Thukral, A., Innocenti, M.: A sliding mode missile pitch autopilot synthesis for high angle of attack maneuvering. IEEE Trans. Control Syst. Technol. 6, 359–371 (1998)
Tournes, C., Shtessel, Y., Shkolnikov, I.: Autopilot for missiles steered by aerodynamic lift and divert thrusters using nonlinear dynamic sliding manifolds. In: AIAA Guidance, Navigation, and Control Conference and Exhibit, pp. 5191–5206. AIAA, San Francisco (2007)
Tournes, C., Shtessel, Y., Shkolnikov, I.: Missile controlled by lift and divert thrusters using nonlinear dynamic sliding manifolds. J. Optim. Theory Appl. 9, 617–625 (2006)
Menon, P.K., Iragavarapu, V.R.: Adaptive techniques for multiple actuator blending. In: AIAA Guidance, Navigation, and Control Conference and Exhibit. AIAA, Boston (1998)
McFarland, M.B., Calise, A.J.: Adaptive nonlinear control of agile anti-air missile using neural net works. IEEE Trans. Control Syst. Technol. 8, 749–756 (2000)
Manable, S.: Application of coefficient diagram method to dual-control surface missile. In: Proc. 15th IFAC Symposium on Automatic Control in Aerospace, Bologna, Italy, pp. 499–504 (2001)
Shima, T., Golan, M.O.: Bounded differential games guidance law for a dual controlled missile. In: Proc. American Control Conf., Denver, Colorado, pp. 390–395 (2003)
Shima, T., Golan, M.O.: Bounded differential games guidance law for dual-controlled missiles. IEEE Trans. Control Syst. Technol. 14, 719–724 (2006)
Shima, T., Golan, M.O.: Linear quadratic differential games guidance law for dual controlled missiles. IEEE Trans. Aerosp. Electron. Syst. 43, 834–842 (2007)
Shima, T., Golan, M.O.: End-games guidance laws for dual-control missiles. Proc. Mech. Part G, J. Aerosp. Eng. 219, 157–170 (2005)
Liu, Y., Qi, N., Lü, R., Zhou, Q.: Bounded linear quadratic differential games guidance law for dual-thrusters controlled missiles. Trans. Jpn. Soc. Aeronaut. Space Sci. 55, 68–76 (2012)
Li, Y., Qi, N., Zhang, W., Wang, X.: Bounded differential guidance law for interceptor missiles with aero-fins and reaction-jets. Trans. Jpn. Soc. Aeronaut. Space Sci. 53, 275–282 (2011)
Li, Y., Qi, N.: Logic-based guidance law for interceptor missiles steered by aerodynamic lift and divert thruster. IEEE Trans. Control Syst. Technol. 19, 884–890 (2011)
Shima, T.: Capture zones in a pursuit-evasion game. In: Proc. 42nd IEEE Conf. Decision Control, Hawaii, pp. 5450–5455 (2003)
Shima, T.: Capture conditions in a pursuit-evasion game between players with biproper dynamics. J. Optim. Theory Appl. 126, 503–527 (2005)
Acknowledgements
The authors express their gratitude to the anonymous reviewers for their detailed revisions and very helpful comments. This research was partially supported by the China Aerospace Science and Institute Corporation.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Josef Shinar.
Rights and permissions
About this article
Cite this article
Liu, Y., Qi, N. & Tang, Z. Effects of Divert-Thrusters on Homing Performance of Endo-atmospheric Interceptors. J Optim Theory Appl 156, 345–364 (2013). https://doi.org/10.1007/s10957-012-0119-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10957-012-0119-1