# POLYNOMIAL FUNCTION BASED GUIDANCE FOR IMPACT ANGLE AND TIME CONTROL

• KIM, TAE-HUN (DEPARTMENT OF GUIDANCE AND CONTROL, AGENCY FOR DEFENSE DEVELOPMENT)
• Accepted : 2015.08.19
• Published : 2015.09.25

#### Abstract

In this paper, missile homing guidance laws to control the impact angle and time are proposed based on the polynomial function. To derive the guidance commands, we first assume that the acceleration command profile can be represented as a polynomial function with unknown coefficients. After that, the unknown coefficients are determined to achieve the given terminal constrains. Using the determined coefficients, we can finally obtain the state feedback guidance command. The suggested approach to design the guidance laws is simple and provides the more generalized optimal solutions of the impact angle and time control guidance.

#### References

1. M. Kim and K. V. Grider, Terminal Guidance for Impact Attitude Angle Constrained Flight Trajectories, IEEE Transactions on Aerospace and Electronic Systems, 9(6) (1973), 852-859.
2. T. L. Song, S. J. Shin and H. Cho, Impact Angle Control for Planar Engagements, IEEE Transactions on Aerospace and Electronic Systems, 35(4) (1999), 1439-1444. https://doi.org/10.1109/7.805460
3. C. K. Ryoo, H. Cho and M. J. Tahk, Optimal Guidance Laws with Terminal Impact Angle Constraint, Journal of Guidance, Control, and Dynamics, 28(4) (2005), 724-732. https://doi.org/10.2514/1.8392
4. C. K. Ryoo, H. Cho and M. J. Tahk, Time-to-Go Weighted Optimal Guidance with Impact Angle Constraints, IEEE Transactions on Control Systems Technology, 14(3) (2006), 483-492. https://doi.org/10.1109/TCST.2006.872525
5. Y. I. Lee, C. K. Ryoo, and E. Kim, Optimal Guidance with Constraints on Impact Angle and Terminal Acceleration, AIAA Guidance, Navigation, and Control Conference, Austin, Texas, 2003.
6. B. S. Kim, J. G. Lee and H. S. Han, Biased PNG Law for Impact Angular Constraint, IEEE Transactions on Aerospace and Electronic Systems, 34(1) (1998), 277-288. https://doi.org/10.1109/7.640285
7. A. Ratnoo and D. Ghose, Impact Angle Constrained Interception of Stationary Targets, Journal of Guidance, Control, and Dynamics, 31(6) (2008), 1816-1821.
8. A. Ratnoo and D. Ghose, Impact Angle Constrained Guidance Against Nonstationay Nonmaneuvering Targets, Journal of Guidance, Control, and Dynamics, 32(1) (2010), 269-275.
9. A. Ratnoo and D. Ghose E, State-Dependent Riccati-Equation-Based Guidance Law for Impact-Angle- Constrained Trajectories, Journal of Guidance, Control, and Dynamics, 32(1) (2009), 320-325. https://doi.org/10.2514/1.37876
10. I. Rusnak, H. Weiss, R. Eliav, and T. Shima, Missile Guidance with Constrained Terminal Body Angle, 2010, IEEE 26-th Convention of Electrical and Electronics Engineers in Israel, Nov. 2010.
11. T. L. Song and S. J. Shin, Time-Optimal Impact Angle Control for Vertical Plane Engagements, EEE Trans. on Aerospace and Electronic Systems, 35(2) (1999), 738-742. https://doi.org/10.1109/7.766954
12. K. S. Kim, B. Jung, and Y. Kim, Practical guidance law controlling impact angle, Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 221(1) (2007), 29-36.
13. J. I. Lee, B. M. Min, and M. J. Tahk, Suboptimal Guidance Laws with Terminal Jerk Constraint, International Conference on Control, Automation and Systems 2007, Seoul, Korea, 2007.
14. B. M. Min, M. J. Tahk, D. H. Shim, and H. C. Bang, Guidance Law for Vision-Based Automatic Landing of UAV, international Journal of Aeronautical and Space Sciences, 8(1) (2007), 46-53. https://doi.org/10.5139/IJASS.2007.8.1.046
15. P. Zarchan, Tactical and Strategic Missile Guidance, 2nd Edition, Washington, DC, 1994.
16. A. E. Bryson Jr. and Y. -C. Ho, Applied Optimal Control, New York: Wiley, pp. 154-155, 1975.
17. F. L. Lewis, Optimal Control, New York: Wiley, 1986.
18. E. Kreindler, Optimality of Proportional Navigation, AIAA Journal, 11(6) (1973), 878-880. https://doi.org/10.2514/3.50527
19. I. S. Jeon, J. I. Lee, and M. J. Tahk, Impact-Time-Control Guidance Law for Anti-Ship Missiles, IEEE Trans. on Control Systems Technology, 14(2) (2006), 260-266. https://doi.org/10.1109/TCST.2005.863655
20. J. I. Lee, I. S. Jeon, and M. J. Tahk, Guidance Law to Control Impact Time and Angle, IEEE Trans. on Aerospace and Electronic Systems, 43(1) (2007), 301-310. https://doi.org/10.1109/TAES.2007.357135
21. I. S. Jeon, J. I. Lee, and M. J. Tahk, Homing Guidance Law for Cooperative Attack of Multiple Missiles, Journal of Guidance, Control, and Dynamics, 33(1) (2010), 275-280. https://doi.org/10.2514/1.40136
22. Y. Zhang, D. Yu, Y. A. Zhang, and Y. Wu, An Impact-Time-Control Guidance Law for Multi-Missiles, Intelligent Computing and Intelligent Systems, ICIS 2009 Conference, Shanghai, 2009.
23. B. Jung and Y. Kim, Guidance Laws for Anti-Ship Missiles Using Impact Angle and Impact Time, AIAA Guidance, Navigation, and Control Conference, Keystone, Colorado, 2006.
24. N. Harl and S. N. Balakrishnan, Impact Time and Angle Guidance with Sliding Mode Control, AIAA Guidance, Navigation, and Control Conference, Chicago, Illinois, 2009.
25. J. I. Lee, I. S. Jeon and M. J. Tahk, Guidance Law Using Augmented Trajectory-Reshaping Command for Salvo Attack of Multiple Missiles, UKACC International Control Conference 2006, Glasgow, Scotland, 2006.
26. E. Kreyszig, Advanced Engineering Mathematics, 9th Edition, Wiley, 2005.
27. I. S. Jeon, Impact-Time-Control Guidance Laws for Cooperative Attack of Multiple Missiles, Ph. D. Thesis, KAIST, Deajeon, Republic of Korea.
28. J. I. Lee, Advanced Missile Guidance Laws for Enhancing Survivability, Ph. D. Thesis, KAIST, Daejeon, Republic of Korea.
29. A. Jameson and E. Kreindler, Inverse problem of linear optimal control, SIAM J. Control, 11(1) (1973), 1-19. https://doi.org/10.1137/0311001
30. J. I. Lee and Y. I. Lee, Inverse optimal problem for homing guidance with angular constraint, J. Korean Society for Aeronautical and Space Science, 35(5) (2007), 412-418. https://doi.org/10.5139/JKSAS.2007.35.5.412