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An optimal control approach to spacecraft rendezvous on elliptical orbit
Author(s) -
Gao Xiangyu,
Teo Kok Lay,
Duan GuangRen
Publication year - 2014
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2108
Subject(s) - rendezvous , linear quadratic regulator , control theory (sociology) , lyapunov function , spacecraft , lyapunov equation , controller (irrigation) , basis (linear algebra) , orbit (dynamics) , mathematics , optimal control , elliptic orbit , parametric statistics , stability theory , computer science , mathematical optimization , control (management) , physics , engineering , nonlinear system , aerospace engineering , geometry , agronomy , statistics , classical mechanics , quantum mechanics , artificial intelligence , biology
Summary In this paper, we consider a linear quadratic regulator control problem for spacecraft rendezvous in an elliptical orbit. A new spacecraft rendezvous model is established. On the basis of this model, a linear quadratic regulator control problem is formulated. A parametric Lyapunov differential equation approach is used to design a state feedback controller such that the resulting closed‐loop system is asymptotically stable, and the performance index is minimized. By an appropriate choice of the value of a parameter, an approximate state feedback controller is obtained from a solution to the periodic Lyapunov differential equation, where the periodic Lyapunov differential equation is solved on the basis of a new numerical algorithm. The spacecraft rendezvous mission under the controller obtained will be accomplished successfully. Several illustrative examples are provided to show the effectiveness of the proposed control design method. Copyright © 2014 John Wiley & Sons, Ltd.