Browse > Article
http://dx.doi.org/10.12941/jksiam.2015.19.217

A TUTORIAL ON LINEAR QUADRATIC OPTIMAL GUIDANCE FOR MISSILE APPLICATIONS  

TAHK, MIN-JEA (DEPARTMENT OF AEROSPACE ENGINEERING, KAIST)
Publication Information
Journal of the Korean Society for Industrial and Applied Mathematics / v.19, no.3, 2015 , pp. 217-234 More about this Journal
Abstract
In this tutorial the theoretical background of LQ optimal guidance is reviewed, starting from calculus of variations. LQ optimal control is then introduced and applied to missile guidance to obtain the basic form of LQ optimal guidance laws. Extension of LQ optimal guidance methodology for handling weighted cost function, dynamic lag associated with the missile dynamics and the autopilot, constrained impact angle, and constrained impact time is also described with a brief discussion on the asymptotic properties of the optimal guidance laws. Furthermore, an introduction to polynomial guidance and generalized impactangle-control guidance, which are closed related with LQ optimal guidance, is provided to demonstrate the current status of missile guidance techniques.
Keywords
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 A. E. Bryson and Y.-C. Ho, Applied Optimal Control, Wiley, New York, 1975.
2 A. E. Bryson, Linear feedback solution for minimum effort interception, rendezvous, and soft landing, AIAA J., 3(8) (1965), 1542-1544.   DOI
3 E. Kreindler, Optimality of proportional navigation, AIAA J., 11(6) (1973), 878-880.   DOI
4 H. Cho, Navigation constants in PNG law and the associated optimal control problems (in Korean), Proc. Korean Automatic Control Conference, Seoul, Korea, 1992, 578-583.
5 C. K. Ryoo, H. Cho, and M. J. Tahk, Time-to-go weighted optimal guidance with impact angle constraints, IEEE T. Contr. Syst. T., 14(3) (2006), 483-492.   DOI   ScienceOn
6 C. H. Lee, M. J. Tahk, and J. I. Lee, Generalized formulation of weighted optimal guidance laws with impact angle constraint IEEE T. Aero. Elec. Sys., 49(2) (2013), 1317-1312.   DOI   ScienceOn
7 M. Y. Ryu, C. H. Lee, and M. J. Tahk, New trajectory shaping guidance laws for anti-tank guided missile, P. I. Mech. Eng. G- J. Aer., 229(7) (2015), 1360-1368.
8 R. G. Cottrell, Optimal intercept guidance for short-range tactical missiles AIAA J., 9(7) (1971), 1414-1415.   DOI
9 C. K. Ryoo, H. Cho, and M. J. Tahk, Optimal guidance laws with terminal impact angle constraint, J. Guid. Contr. Dyn., 28(4) (2005), 724-732.   DOI   ScienceOn
10 M. J. Tahk, C. K. Ryoo and H. Cho, Recursive time-to-go estimation for homing guidance missiles, IEEE T. Aero. Elec. Sys., 38(1) (2002), 13-24.   DOI   ScienceOn
11 C. K. Ryoo, H. Cho, and M. J. Tahk, Closed-form solutions of optimal guidance with terminal impact angle constraints, Proceedings of the 2003 IEEE Int. Conf. Contr. Appl., Istanbul, Turkey, June 2003, 504-509.
12 C. K. Ryoo, H. S. Shin, and M. J. Tahk, Energy optimal waypoint guidance synthesis for anti-ship missiles, IEEE T. Aero. Elec. Sys., 46(1) (2010), 80-95.   DOI   ScienceOn
13 H. Cho, C. K. Ryoo, A. Tsourdos, and B. White, Optimal impact angle control guidance law based on linearization about collision triangle, J. Guid. Contr. Dyn., 37(3) (2014), 958-964.   DOI   ScienceOn
14 M. J. Tahk, B. M. Min, and H. C. Shim, Study on the time-to-go polynomial guidance (in Korean), Proc. Spring Conf. Korean Soc. Aero. Space Sci., Yong Pyong, Korea, (2007), 459-462.
15 C. H. Lee, T. H. Kim, M. J. Tahk, and I. H. Whang, Polynomial guidance laws considering terminal impact angle and acceleration constraints, IEEE T. Aero. Elec. Sys., 49(1) (2013), 74-92.   DOI   ScienceOn
16 T. H. Kim, C. H. Lee, M. J. Tahk, and I. S. Jeon, Augmented polynomial guidance with impact time and angle constraints, IEEE T. Aero. Elec. Sys., 49(4) (2013), 2806-2817.   DOI   ScienceOn
17 T. H. Kim, C. H. Lee, and M. J. Tahk, Time-to-go polynomial guidance with trajectory modulation for observability enhancement, IEEE T. Aero. Elec. Sys., 49(1) (2013), 55-73.   DOI   ScienceOn
18 Y. I. Lee, S. H. Kim, and M. J. Tahk, Optimality of linear time-varying guidance for impact angle control, IEEE T. Aero. Elec. Sys., 48(3) (2012), 2808-2817.
19 Y. I. Lee, S. H. Kim, and M. J. Tahk, Analytic solutions of optimal angular constrained guidance for first-order lag system, P. I. Mech. Eng. G- J. Aer., 227(3) (2013), 827-837.
20 Y. I. Lee, S. H. Kim, J. I. Lee, and M. J. Tahk, Analytic Solutions of Generalized Impact-Angle-Control Guidance Law for First-Order Lag System, J. Guid. Contr. Dyn., 36(1) (2013), 96-112.   DOI   ScienceOn
21 C. H. Lee, T. H. Kim, M. J. Tahk, Design of impact angle control guidance laws via high-performance sliding mode control, P. I. Mech. Eng. G- J. Aer., 227(2) (2013), 235-253.
22 I. S. Jeon and J. I Lee, Guidance law to reach circular target area with grazing angle constraint (in Korean), J. Soc. Aero. Space Sci., 36(9) (2008), 884-890.
23 B. G. Park, T. H. Kim, and M. J. Tahk, Optimal impact angle control guidance law considering the seeker's field-of-view limits, P. I. Mech. Eng. G- J. Aer., 227(8) (2013), 1347-1364.
24 I. S. Jeon, J. I. Lee, and M. J. Tahk, Impact-time-control guidance law for anti-ship missiles, IEEE T. Cont. Sys. Tech., 14(2) (2006), 260-266.   DOI   ScienceOn
25 J. I. Lee, I. S. Jeon, and M. J. Tahk, Guidance law to control impact time and angle, IEEE T. Aero. Elec. Sys., 43(1) (2007), 301-310.   DOI   ScienceOn
26 I. S. Jeon, J. I. Lee, and M. J. Tahk, Homing guidance law for cooperative attack of multiple missiles, J. Guid. Contr. Dyn., 33(1) (2010), 275-280.   DOI   ScienceOn
27 M. J. Tahk, B. K. Park, B. C. Sun, I. S. Hwang, H. J. Cho, and T. L. Song, The closed-form solution and its approximation of the optimal guidance law, 12th World Congress of IFAC, Sydney, Australia, July 1993, 207-210.
28 T. Kailath, Linear Systems,Prentice Hall, 1980.