CLC number: O232
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
Crosschecked: 2020-03-06
Cited: 0
Clicked: 5436
Li Xie, Yi-qun Zhang, Jun-yan Xu. Optimal two-impulse space interception with multiple constraints[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(7): 1085-1107.
@article{title="Optimal two-impulse space interception with multiple constraints",
author="Li Xie, Yi-qun Zhang, Jun-yan Xu",
journal="Frontiers of Information Technology & Electronic Engineering",
volume="21",
number="7",
pages="1085-1107",
year="2020",
publisher="Zhejiang University Press & Springer",
doi="10.1631/FITEE.1800763"
}
%0 Journal Article
%T Optimal two-impulse space interception with multiple constraints
%A Li Xie
%A Yi-qun Zhang
%A Jun-yan Xu
%J Frontiers of Information Technology & Electronic Engineering
%V 21
%N 7
%P 1085-1107
%@ 2095-9184
%D 2020
%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.1800763
TY - JOUR
T1 - Optimal two-impulse space interception with multiple constraints
A1 - Li Xie
A1 - Yi-qun Zhang
A1 - Jun-yan Xu
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 21
IS - 7
SP - 1085
EP - 1107
%@ 2095-9184
Y1 - 2020
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/FITEE.1800763
Abstract: We consider optimal two-impulse space interception problems with multiple constraints. The multiple constraints are imposed on the terminal position of a space interceptor, impulse and impact instants, and the component-wise magnitudes of velocity impulses. These optimization problems are formulated as multi-point boundary value problems and solved by the calculus of variations. Slackness variable methods are used to convert all inequality constraints into equality constraints so that the Lagrange multiplier method can be used. A new dynamic slackness variable method is presented. As a result, an indirect optimization method is developed. Subsequently, our method is used to solve the two-impulse space interception problems of free-flight ballistic missiles. A number of conclusions for local optimal solutions have been drawn based on highly accurate numerical solutions. Specifically, by numerical examples, we show that when time and velocity impulse constraints are imposed, optimal two-impulse solutions may occur; if two-impulse instants are free, then a two-impulse space interception problem with velocity impulse constraints may degenerate to a one-impulse case.
[1]Ben-Asher JZ, 2010. Optimal Control Theory with Aerospace Applications. American Institute of Aeronautics and Astronautics, Inc., Reston, Virginia, USA.
[2]Bryson AE, 1980. This Week’s Citation Classic. http://garfield.library.upenn.edu/classics1980/A1980JE 96000001.pdf
[3]Bryson AE, 1996. Optimal control—1950 to 1985. IEEE Contr Syst Mag, 16(3):26-33.
[4]Bryson AE, Ho YC, 1975. Applied Optimal Control: Optimization, Estimation and Control. Halsted Press, New York, USA.
[5]Guidance and Optimal Control of Ballistic Missiles. National University of Defense Technology Press, Changsha, China (in Chinese).
[6]Colasurdo G, Pastrone D, 1994. Indirect optimization method for impulsive transfers. Proc Astrodynamics Conf on Guidance, Navigation, and Control, p.441-448.
[7]Curtis HD, 2014. Orbital Mechanics for Engineering Students (3rd Ed.). Elsevier, Oxford, UK.
[8]Gobetz FW, Doll JR, 1969. A survey of impulsive trajectories. AIAA J, 7(5):801-834.
[9]Guidance Law of Interception Problems. National Defense Industry Press, Beijing, China (in Chinese).
[10]Hull DG, 2003. Optimal Control Theory for Applications. Springer, New York, USA.
[11]Jezewski DJ, 1975. Primer Vector Theory and Applications. NASA-TR-R-454, NASA, Washington, USA.
[12]Kierzenka J, 1998. Studies in the Numerical Solution of Ordinary Differential Equations. PhD Thesis, Department of Mathematics, Southern Methodist University, Dallas, USA.
[13]Kierzenka J, Shampine LF, 2001. A BVP solver based on residual control and the Matlab PSE. ACM Trans Math Softw, 27(3):299-316.
[14]Kierzenka J, Shampine LF, 2008. A BVP solver that controls residual and error. J Numer Anal Ind Appl Math, 3:27-41.
[15]Lawden DF, 1964. Optimal trajectories for space navigation. Math Gaz, 48(36):478-479.
[16]Longuski JM, Guzmán JJ, Prussing JE, 2014. Optimal Control with Aerospace Applications. Springer, New York, USA.
[17]Luo YZ, Tang GJ, Lei YJ, et al., 2007. Optimization of multiple-impulse, multiple-revolution, rendezvous-phasing maneuvers. J Guid Contr Dynam, 30(4):946-952.
[18]Luo YZ, Zhang J, Li HY, et al., 2010. Interactive optimization approach for optimal impulsive rendezvous using primer vector and evolutionary algorithms. Acta Astronaut, 67(3-4):396-405.
[19]Prussing JE, 1995. Optimal impulsive linear systems: sufficient conditions and maximum number of impulses. J Astronaut Sci, 43(2):195-206.
[20]Prussing JE, 2010. Primer vector theory and applications. In: Conway BA (Ed.), Spacecraft Trajectory Optimization. Cambridge University Press, Cambridge, UK, p.16-36.
[21]Prussing JE, Chiu JH, 1986. Optimal multiple-impulse time-fixed rendezvous between circular orbits. J Guid Contr Dynam, 9(1):17-22.
[22]Qin HS, Wang CZ, 1977. Guidance Problems of Exoatmospheric Interception and Rendezvous (Collected Papers). National Defense Industry Press, Beijing, China (in Chinese).
[23]Robinson AC, 1967. Comparison of Fuel-Optimal Maneuvers Using a Minimum Number of Impulses with Those Using the Optimal Number of Impulses: a Survey. NASA Contractor Report NASw-1146, Columbus Laboratories, Columbus, USA.
[24]Sandrik SL, 2006. Primer-Optimized Results and Trends for Circular Phasing and Other Circle-to-Circle Impulsive Coplanar Rendezvous. PhD Thesis, University of Illinois at Urbana-Champaign, Urbana-Champaign Urbana, IL, USA.
[25]Shampine LF, Gladwell I, Thompson S, 2003. Solving ODEs with Matlab. Cambridge University Press, Cambridge, UK.
[26]Sigal E, Ben-Asher JZ, 2014. Optimal control for switched systems with pre-defined order and switch-dependent dynamics. J Optim Theory Appl, 161(2):582-591.
[27]Subchan S, .Zbikowski R, 2009. Computational Optimal Control: Tools and Practice. Wiley, Chichester, UK.
[28]Taur DR, Coverstone-Carroll V, Prussing JE, 1995. Optimal impulsive time-fixed orbital rendezvous and interception with path constraints. J Guid Contr Dynam, 18(1):54-60.
[29]Tsien HS, Evans RC, 1951. Optimum thrust programming for a sounding rocket. J Am Rocket Soc, 21(5):99-107.
[30]Vinh NX, Lu P, Howe RM, et al., 1990. Optimal interception with time constraint. J Optim Theory Appl, 66(3):361-390.
[31]Wang XH, Huang Y, Wang H, et al., 2014. Variable time impulse system optimization with continuous control and impulse control. Asian J Contr, 16(1):107-116.
[32]Xie L, Zhang YQ, Xu JY, 2018. Hohmann transfer via constrained optimization. Front Inform Technol Electron Eng, 19(11):1444-1458.
[34]Žefran M, Desai JP, Kumar V, 1996. Continuous motion plans for robotic systems with changing dynamic behavior. Proc 2nd Int Workshop on Algorithmic Foundations of Robotics.
Open peer comments: Debate/Discuss/Question/Opinion
<1>