Modares Mechanical Engineering

Modares Mechanical Engineering

Optimization of Planar Low-Thrust Orbit Transfer Maneuver via Fuzzy Optimal Control Approach

Authors
Amir Reza Kosari
Seyed Aliakbar Razavi
Hadi Jahanshahi
Abstract
In this paper, minimum-time low-thrust planar orbit transfer problem is solved by fuzzy optimal control. Trajectory dynamic restricting assumptions and using analytical averaging method, the governing equations of orbit transfer problem in its desired form with constant acceleration magnitude is achieved. Then, using Euler discretization method, the whole differential dynamic equations, performance function and transversality conditions are represented in a discrete form. Calling membership function concept of fuzzy environment, this algorithm transfers classical optimal control including performance index and trajectory transversality conditions associated with uncertanities to fuzzy environment. Thereafter, introducing slack variables all the inequalities change to equality conditions. Applying Bellman-Zadeh approach, optimal control problem turns to parameter optimization problem which then is solved by Lagrange multipliers technique. Finally, solving the set of nonlinear algebraic equations made by optimality necessary conditions simultaneously is achieved by nonlinear programming method. Numerical fuzzy optimal control results are validated with available analytical results which show the priorities of this method in orbit transfer trajectory optimization in presence of uncertainities. FOC approach is categorized into direct methods for solving optimal control problems, while it is far from their defects e.g. curse of dimensionality and burdensome computational load so that it applies fuzzy approach and expert knowledge to simply solve the problems.
Keywords
Planar Orbit Transfer Problem
Minimum-Time Problem
Fuzzy Optimal Control
Transversality Condition
[1] S. Pourtakdoust, M. Jalali, Thrust-limited optimal threedimensional
spacecraft trajectories, International Journal of
Engineering, Vol. 14, No. 1, pp. 81-90, 2001.
[2] A. A. Naeeni, J. Roshanian, Developing a hybrid algorithm to
design the optimal trajectory of reentry vehicles, Modares
Mechanical Engineering, Vol. 14, No. 13, pp. 143-152, 2015. (in
Persian (فارسی
[3] E. Maani, A. Kosari, M. Fakoor, Two-objective optimization of
GEO communication satellite trajectory considering continuous
orbital maneuver, Modares Mechanical Engineering, Vol. 13, No.
7, pp. 142-152, 2013. (in Persian (فارسی
[4] E. Maani, A. Kosari, M. Fakoor, Two-objective optimization of
GEO communication satellite trajectory considering impulsive
orbital maneuver, Modares Mechanical Engineering, Vol. 14, No.
5, pp. 121-128, 2014. (in Persian (فارسی
[5] M. Navabi, M. Sanatifar, Optimal impulsive orbital transfer
between coplanar-noncoaxial orbits, local and global solutions, 5th
International Conference on Recent Advances in Space
Technologies (RAST), Istanbul, Turkey, June 9-11, 2011.
[6] M. Navabi, E. Meshkinfam, Space low-thrust trajectory
optimization utilizing numerical techniques, a comparative study,
6th International Conference on Recent Advances in Space
Technologies (RAST), Istanbul, Turkey, June 12-14, 2013.
[7] Y. Ulybyshev, Continuous thrust orbit transfer optimization using
large-scale linear programming, Journal of Guidance, Control, And
Dynamics, Vol. 30, No. 2, pp. 427-436, 2007.
[8] J. Gergaud, T. Haberkorn, Orbital transfer: Some links between the
low-thrust and the impulse cases, Acta Astronautica, Vol. 60, No. 8,
pp. 649-657, 2007.
[9] G. Yang, Direct optimization of low-thrust many-revolution earthorbit
transfers, Chinese Journal of Aeronautics, Vol. 22, No. 4, pp.
426-433, 2009.
[10] T. N. Edelbaum, Propulsion requirements for controllable satellites,
ARS Journal, Vol. 31, No. 8, pp. 1079-1089, 1961.
[11] J. A. Kechichian, Reformulation of Edelbaum's low-thrust transfer
problem using optimal control theory, Journal of Guidance,
Control, and Dynamics, Vol. 20, No. 5, pp. 988-994, 1997.
[12] J. A. Kéchichian, Optimal altitude-constrained low-thrust transfer
between inclined Circular Orbits, The Journal of the Astronautical
Sciences, Vol. 54, No. 3-4, pp. 485-503, 2006.
[13] J. A. Kéchichian, Optimal low-thrust transfer in general circular
orbit using analytic averaging of the system dynamics, The Journal
of the Astronautical Sciences, Vol. 57, No. 1-2, pp. 369-392, 2009.
Modares Mechanical Engineering
Volume 17, Issue 1
March 2017
Pages 1-10