The interception of high-speed target with an arbitrary maneuvering acceleration causes serious troubles to the guidance and control system design of airborne missile. A novel guidance law based on the classical differential geometry curve theory was proposed not long ago. Although it is believed and numerically demonstrated that this differential geometric guidance law (DGGL) is superior to the classical pure proportional navigation (PPN) in intercepting high-speed targets, its performance has not been thoroughly analyzed. In this paper, using the Lyapunov-like approach, the performance of DGGL against the high-speed target with an arbitrary but upper-bounded maneuvering acceleration is well studied. The upper bounds of the LOS rate and commanded acceleration of DGGL are obtained, and conditions that guarantee the capture of this type of maneuvering target are also presented. The nonlinear relative dynamics between the missile and target is taken into full account. Finally, the proposed theoretical findings are demonstrated by numerical simulation examples.
Kuroda T and Imado F. Advanced missile guidance system against very high speed target. In: AIAA guidance, navigation and control conference, Minneapolis, MN, August 1988, pp.320–324.
2.
Yuan PJ. Anti-missile guidance. Chun Shan Institute of Science and Technology, Technical Report, 2007.
3.
LinCLHungHZ. Development of an integrated fuzzy-logic-based missile guidance law against high speed target. IEEE Transact Fuzzy Syst2004; 12: 157–169.
4.
Tyan F and Jeng FS. Capture region of a three dimensional PPN guidance law against a high speed-nonmaneuvering target. In: Proceedings of the 2008 American Control Conference, Seattle, Washington, USA, 11–13 June 2008.
5.
Tyan F. Capture region for PPN guidance law with observer lag. In: Proceedings of 2011 8th Asian control conference (ASCC), Kaohsiung, Taiwan, 15–18 May 2011.
6.
Golan OM, Rom H and Yehezkely O. System for destroying ballistic missiles. Patent 6,209,820 B1, USA, 2001.
7.
Golan OM and Shima T. Head pursuit guidance for hypervelocity interception. In: AIAA guidance, navigation, and control conference and exhibit, Providence, RI, AIAA Paper 2004-4885, 2004.
8.
GolanOMShimaT. Head pursuit guidance. J Guid Control Dynam2007; 30: 1437–1444.
9.
ShimaT. Interceptor angle guidance. J Guidance Control Dynam2011; 34: 484–492.
10.
PrasannaHMGhoseD. Retro-proportional-navigation: a new guidance law for interception of high speed targets. J Guid Control Dynam2012; 35: 377–386.
11.
YanLZhaoJGShenHRet al.Biased retro-proportional navigation law for interception of high-speed targets with angular constraint. Defense Technol2014; 10: 60–65.
12.
GhoshSGhoseDRahaS. Capturability analysis of a 3-D Retro-PN guidance law for higher speed nonmaneuvering targets. IEEE Transact Control Syst Technol2014; 22: 1864–1874.
13.
GhoshSGhoseDRahaS. Composite guidance for impact angle control against higher speed targets. J Guid Control Dynam2016; 39: 98–117.
14.
StruikDJ. Lectures on classical differential geometry, New York, NY: Dover, 1988, pp. 10–20.
Serakos D and Lin CF. Three dimensional mid-course guidance state equations. In: Proceedings of the 1999 American Control Conference, San Diego, California, USA, 2–4 June 1999.
18.
ChiouYCKuo CY. Geometric approach to three dimensional missile guidance problems. J Guid Control Dynam1998; 21: 335–341.
19.
ChiouYCKuoCY. Geometric analysis of missile guidance command. IEEE Proc: Control Theory Appl2000; 147: 205–211.
20.
KuoCYSoetantoDChiouYC. Geometric analysis of flight control command for tactical missile guidance. IEEE Transact Control Syst Technol2001; 9: 234–243.
21.
AriffOZbikowskiRTsourdosAet al.Differential geometric guidance based on the involute of the target's trajectory. J Guid Control Dynam2005; 28: 990–996.
22.
WhiteBAZbikowskiRTsourdosA. Direct intercept guidance using differential geometric concepts. IEEE Transact Aerosp Electronic Syst2007; 43: 899–919.
23.
LiCYJingWXWangHet al.Iterative solution to differential geometric guidance problem. Aircraft Eng Aerosp Technol2006; 78: 415–425.
24.
Shneydor NA. Missile guidance and pursuit – kinematics, dynamics and control. Chichester: Horwood Publishing, 1998, Appendix A.
25.
LiKBChenLBaiXZ. Differential geometric modeling of guidance problem for interceptors. Sci China Tech Sci2011; 54: 2283–2295.
26.
LiKBChenLTangGJ. Improved differential geometric guidance commands for endoatmospheric interception of high-speed targets. Sci China Tech Sci2013; 56: 518–528.
27.
LiKBChenLTangGJ. Algebraic solution of differential geometric guidance command and time delay control. Sci China Tech Sci2015; 58: 565–573.
28.
Li KB, Su WS and Chen L. Performance analysis of three-dimensional differential geometric guidance law against low-speed maneuvering targets. Astrodynamics 2018; 2: 233–247.
29.
LiCYJingWXWangHet al.A novel approach to 2D differential geometric guidance problem. Transact Japan Soc Aeronaut Space Sci2007; 50: 34–40.
30.
LiCYJingWX. Fuzzy PID controller for 2D differential geometric guidance and control problem. IET Control Theory Appl2007; 1: 564–571.
DhananjayNGhoseDBhatMS. Capturability of a geometric gudiance law in relative velocity space. IEEE Transact Control Syst Technol2009; 17: 111–122.
33.
WangWLChenLLiKBet al.One active debris removal system design and error analysis. Acta Astronaut2016; 128: 499–512.
34.
MengYHChenQFNiQ. A new geometric guidance approach to spacecraft near-distance rendezvous problem. Acta Astronaut2016; 129: 374–383.
35.
JosephZAsherB. New proportional navigation law for ground-to-air systems. J Guid Control Dynam2003; 23: 822–825.
36.
LiCYJingWX. Analysis of 3D geometric guidance problem. Transact Japan Soc Aeronaut Space Sci2008; 51: 124–129.
37.
HaJHurJSKoMSet al.Performance analysis of PNG laws for randomly maneuvering targets. IEEE Transact Aerosp Electronic Syst1990; 26: 713–721.
38.
KimBSLeeJGHanHS. Biased PNG law for impact with angular constraint. IEEE Transact Aerosp Electronic Syst1998; 34: 277–288.
39.
SongSHHa IJ. A Lyapunov-like approach to performance analysis of 3-dimension pure PNG laws. IEEE Transact Aerosp Electronic Syst1994; 30: 238–248.
40.
OhJHHaIJ. Capturability of the three-dimensional pure PNG Law. IEEE Transact Aerosp Electronic Syst1999; 35: 491–503.
41.
MurtaughSACrielHE. Fundamentals of proportional navigation. IEEE Spectrum1966; 3: 75–85.
42.
TyanF. Unified approach to missile guidance laws: a 3D extension. IEEE Transact Aerosp Electronic Syst2005; 41: 1178–1199.
43.
TyanF. Capture region of a GIPN guidance law for missile and target with bounded maneuverability. IEEE Transact Aerosp Electronic Syst2011; 47: 201–213.
44.
TyanF. Analysis of 3D PPN guidance laws for nonmaneuvering target. IEEE Transact Aerosp Electronic Syst2015; 51: 2932–2943.
45.
LiKBSuWSChenL. Performance analysis of realistic true proportional navigation against maneuvering targets using Lyapunov-like approach. Aerosp Sci Technol2017; 69: 333–341.
46.
LiKBLiangYGSuWSet al.Performance of 3D TPN against true-arbitrarily maneuvering target for exoatmospheric interception. Sci China Tech Sci2008; 61: 1161–1174.
