# OPTIMAL IMPACT ANGLE CONTROL GUIDANCE LAWS AGAINST A MANEUVERING TARGET

• Accepted : 2015.08.24
• Published : 2015.09.25

#### Abstract

Optimal impact angle control guidance law and its variants for intercepting a maneuvering target are introduced in this paper. The linear quadratic(LQ) optimal control theory is reviewed first to setup framework of guidance law derivation, called the sweep method. As an example, the inversely weighted time-to-go energy optimal control problem to obtain the optimal impact angle control guidance law for a fixed target is solved via the sweep method. Since this optimal guidance law is not applicable for a moving target due to the angle mismatch at the impact instant, the law is modified to three different biased proportional navigation(PN) laws: the flight path angle control law, the line-of-sight(LOS) angle control law, and the relative flight path angle control law. Effectiveness of the guidance laws are verified via numerical simulations.

#### 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. A. E. Bryson Jr. and Y.-C. Ho, Applied Optimal Control, Wiley, New York, 1975.
3. C. K. Ryoo, H. Cho, and M. J. Tahk, Optimal Guidance Laws with Terminal Impact Angle Constraints, 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. E. J. Ohlmeyer and C. A. Phillips. Generalized Vector Explicit Guidance, Journal of Guidance, Control, and Dynamics, 29(2) (2006), 261-268. https://doi.org/10.2514/1.14956
6. C. K. Ryoo, H. S. Shin, and M. J. Tahk, Energy Optimal Waypoint Guidance Synthesis for Anti-Ship Missiles, IEEE Transactions on Aerospace and Electronic Systems, 46(1) (2010), 80-95. https://doi.org/10.1109/TAES.2010.5417149
7. H. Cho, Lecture note for Linear Optimal Control Theory(private), 1993.
8. D. E. Kirk, Optimal Control Theory - An Introduction, Prentice-Hall, Englewood Cliffs, New Jersey, 1970.
9. D. G. Hull, Optimal Control Theory for Applications, Springer-Verlag, 2003.
10. H. Cho, C. K. Ryoo, A. Tsourdos, and B. White, Optimal Impact Angle Control Guidance Law Based on Linearization about Collision Triangle, Journal of Guidance, Control, and Dynamics, 37(3) (2014). 958-964. https://doi.org/10.2514/1.62910