An Optimal Soft Landing Control for Moon Lander by Means of Measures


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Designing a new control strategy for a moon lander to achieve an optimal soft landing, is the main purpose of this paper. For the dynamical system of the propeller to achieve the lowest level of fuel consumption, the problem of soft landing is presented as an optimal control one. Representing this into a variational form, transferring to an optimization problem on a measure space and then determining the optimal solution via a linear programming problem is the new solution path. This method has some important advantages in compare with the other, which are explain within a numerical simulation.



Edited by:

Zhou Mark




J.A. Fakharzadeh and S. Salehi, "An Optimal Soft Landing Control for Moon Lander by Means of Measures", Applied Mechanics and Materials, Vols. 52-54, pp. 1861-1867, 2011

Online since:

March 2011




[1] E.J., Andersonand an P., Nash: Linear Programming in Infinite Dimensional Space, Theory and Application, John Wiley and Sons(1987).

[2] J. A., Fakharzadeh and J . E., Rubio: Best Domain for an Elliptic Problem in Cartesian Coordinates by Means of Shape-Measure, Asian Journal Of Control, Vol. 11, pp.536-547(2009).


[3] M., Gachpazan, B. A. Hashemi and K.A., Vahidian: A Measure –Theoretical Approach for Solving Discrete Optimal Control Problems, Applied Mathematics and Computation, Vol. 173, PP 736-752(2006).


[4] C.D., Hyun, B., Jeong, D., Lee and H., Bang : Optimal Perilune Altitude of Lunar Landing Trajectory, Int'l J. of Aeronautical & Space Sciences, Vol. 10, PP 67-74(2009).


[5] Y., Kianand and M., Ernst Analysis of Parking Orbits and Transfer Trajectories for Mission Design of CIS-Lunar Space Stations: Acta Astronautica, Vol. 55, PP 759-771, (2004).


[6] X. L., Liuand and G. R., Duan: Nonlinear Optimal Control for the Soft Landing of Lunar Lander , Proceeding Of 1st International Symposium On Systems And Control In Aerospace And Astronautics. Harbin, China, pp.1382-1387(2006).


[7] G. R., LiuDuan and K.L., Teo: Optimal Soft Landing Control for Moon Lander, Automatica, Vol 44, pp.1097-1103(2008).


[8] V.R., Ramanan and Madan., Lal: Analysis of Optimal Strategies for Soft Landing on the Moon Lander from Lunar Parking Orbits, Earth Syst. Sci., Vol. 114, PP 807-813, (2005).


[9] R ., Resnick, D., Halliday and S.K., Krane: Physics (4th Edition), Volume 1, (1992).

[10] J. E., Rubio: Control and Optimization, the linear treatment of nonlinear problems. Manchester University Press, Manchester(1986).

[11] J. E., Rubio : Modern Trends In The Calculus Of Variations and Optimal Control Theory, In R . Geise, editor, Vortagsauszuge, Mathematiker Kongress, Berlin, Mathematische Gesellschaft, PP 155-163(1990).

[12] W., Rudin : Real and Complex Analysis, Tata McGraw-Hill Publishing Co. Ltd , New Delhi (1983).

[13] D., Wang, X., Huang and Y., Guan : GNC System Scheme for Lunar Soft Landing Spacecraft, Advances in Space Research, Vol. 42, PP 379-385(2008).


[14] D.Y., Wang, T.S., Y. A., Liand Hui: Sub-Optimal Fuel Guidance Law for Lunar Soft Landing, Journal Of Astronautics, Vol. 21, pp.55-63(2000).