Due to the complexity and inconstancy of the space environment, accurate mathematical models for spacecraft rendezvous are difficult to retrieve, which consequently complicates the control tasks. In this paper, a linearized time-varying plant model with consideration of the external perturbations is developed to approximate the spacecraft rendezvous in near-circular orbits. In order to achieve the robust stability with optimal performance cost, a partially independent control scheme is proposed, which consists of a robust anti-windup controller for the in-plane motion and a H∞ controller for the out-of-plane motion. The effectiveness and advantages of the partially independent control scheme are verified by comparing with other control schemes in a numerical example.
CarterTE. State transition matrices for terminal rendezvous studies: Brief survey and new example. J Guid Control Dyn1998; 21: 148–155.
5.
AnthonyMLSasakiFT. Rendezvous problem for nearly circular orbits. AIAA J1965; 3: 1666–1673.
6.
MeltonRG. Time-explicit representation of relative motion between elliptical orbits. J Guid Control Dyn2000; 23: 604–610.
7.
ChangSSLPengTKC. Adaptive guaranteed cost control of systems with uncertain parameters. IEEE Trans Autom Control1972; 17: 474–483.
8.
PetersenIRMcFarlaneDC. Optimal guaranteed cost control and filtering for uncertain linear systems. IEEE Trans Autom Control1994; 39: 1971–1977.
9.
YuLChuJ. An LMI approach to guaranteed cost control of linear uncertain time-delay systems. Automatica1999; 35: 1155–1159.
10.
EsfahaniSHPetersenIR. An LMI approach to the output-feedback guaranteed cost control for uncertain time-delay systems. Int J Robust Nonlinear Control2000; 10: 157–174.
11.
KarimiHRMaralaniPJLohmannB, et al. control of parameter-dependent state-delayed systems using polynomial parameter-dependent quadratic functions. Int J Control2005; 78: 254–263.
12.
LiuDWangDWangFY, et al.Neural-network-based online hjb solution for optimal robust guaranteed cost control of continuous-time uncertain nonlinear systems. IEEE Trans Cybernet2014; 44: 2834–2847.
13.
QiuLYaoFXuG, et al.Output feedback guaranteed cost control for networked control systems with random packet dropouts and time delays in forward and feedback communication links. IEEE Trans Autom Sci Eng2016; 13: 284–295.
14.
MohammadiLAlfiAXuB. Robust bilateral control for state convergence in uncertain teleoperation systems with time-varying delay: A guaranteed cost control design. Nonlinear Dyn2017; 88: 1413–1426.
15.
ZamesG. Feedback and optimal sensitivity: Model reference transformation multiplicative seminorms, and approximate inverse. IEEE Trans Autom Control1981; 26: 301–320.
16.
BarmishBR. Stabilization of uncertain systems via linear control. IEEE Trans Autom Control1983; 28: 848–850.
17.
FrancisBA. A course in H∞ control theory, Berlin: Springer, 1987.
18.
KhargonekarPPPetersenIRZhouK. Robust stabilization of uncertain linear system: Quadratic stability and control theory. IEEE Trans Autom Control1990; 35: 356–361.
19.
BoydSP. Linear matrix inequalities in system and control theory1994; vol. 15, Philadelphia, PA: SIAM.
20.
ChilaliMGahinetP. design with pole placement constraints: An LMI approach. IEEE Trans Autom Control1996; 41: 358–367.
21.
KarimiHRGaoH. Mixed output-feedback control of second-order neutral systems with time-varying state and input delays. ISA Trans2008; 47: 311–324.
22.
DongHWangZDingSX, et al.On estimation of randomly occurring faults for a class of nonlinear time-varying systems with fading channels. IEEE Trans Autom Control2016; 61: 479–484.
23.
ShiPZhangYChadliM, et al.Mixed h-infinity and passive filtering for discrete fuzzy neural networks with stochastic jumps and time delays. IEEE Trans Neural Netw Learn Syst2017; 27: 903–909.
24.
WeiYQiuJShiP, et al.A new design of h-infinity piecewise filtering for discrete-time nonlinear time-varying delay systems via ts fuzzy affine models. IEEE Trans Syst Man Cybernet Syst2017; 47: 2034–2047.
25.
Zhao L, Jia Y and Matsuno F. Adaptive time-varying sliding mode control for autonomous spacecraft rendezvous. In: Proceedings of decision and control, Florence, Italy, 10–13 December 2013, pp.5504–5509.
26.
ImaniABeigzadehB. Robust control of spacecraft rendezvous on elliptical orbits: Optimal sliding mode and backstepping sliding mode approaches. Proc IMechE, Part G: J Aerospace Engineering2015; 230: 1975–1989.
27.
GaoHYangXShiP. Multi-objective robust control of spacecraft rendezvous. IEEE Trans Control Syst Technol2009; 17: 794–802.
28.
ZhouYYanYHuangX, et al.Multi-objective and reliable output feedback control for spacecraft hovering. Proc IMechE, Part G: J Aerospace Engineering2014; 229: 1798–1812.
29.
ZhouBLamJ. Global stabilization of linearized spacecraft rendezvous system by saturated linear feedback. IEEE Trans Control Syst Technol2017; 25: 2185–2193.
30.
LiaoFJiHXieY. A nearly optimal control for spacecraft rendezvous with constrained controls. Trans Inst Meas Control2016; 38: 832–845.
31.
LiZLiuMKarimiHR, et al.Sampled-data control of spacecraft rendezvous with discontinuous Lyapunov approach. Math Probl Eng2013. Article ID 814271:10 pages.
32.
LiZLiuMKarimiHR, et al.Observer-based stabilization of spacecraft rendezvous with variable sampling and sensor nonlinearity. Math Probl Eng2013. Article ID 902452:11 pages.
33.
YangXGaoH. Robust reliable control for autonomous spacecraft rendezvous with limited-thrust. Aerosp Sci Technol2013; 24: 161–168.
34.
WanNLiuMKarimiHR. Robust tracking control for rendezvous in near-circular orbits. Math Probl Eng2013. Article ID 726945:11 pages.
35.
WanNLiuMKarimiHR. Observer-based robust control for spacecraft rendezvous with thrust saturation. Abstr Appl Anal2014. Article ID 710850:10 pages.
36.
Wan N, Naidu DS, Liu M, et al. Adaptive sliding mode control for spacecraft rendezvous in near-circular orbits with time-varying saturation constraint. In: Proceedings of American control conference, Seattle, WA, USA, 24–26 May 2017, pp.5812–5817.
37.
WanNYaoWShiM. A composite robust fault-tolerant control scheme for limited-thrust spacecraft rendezvous in near-circular orbits. J Dyn Syst Meas Control2017; 139: 1–12.
38.
GaoXTeoKLDuanGR. Non-fragile guaranteed cost control for robust spacecraft orbit transfer with small thrust. IMA J Math Control Inform2011; 28: 507–524.
39.
CurtisH. Orbital mechanics for engineering students, Oxford: Butterworth-Heinemann, 2005.
40.
YangXGaoH. Guaranteed cost output tracking control for autonomous homing phase of spacecraft rendezvous. J Aerosp Eng2011; 24: 478–487.
41.
LiuRLiuMSunZ, et al.Impulse variance control for spacecraft autonomous rendezvous with an observer-based approach. IMA J Math Control Inform2018; 35: 57–73.
42.
EbrahimiBBahramiMRoshanianJ. Optimal sliding-mode guidance with terminal velocity constraint for fixed-interval propulsive maneuvers. Acta Astronaut2008; 62: 556–562.
43.
ZhouBWangQLinZ, et al.Gain scheduled control of linear systems subject to actuator saturation with application to spacecraft rendezvous. IEEE Trans Control Syst Technol2014; 22: 2031–2038.
44.
ZhangJXiaYZuoZ, et al.Disturbance observer-based integral sliding-mode control for systems with mismatched disturbances. IEEE Trans Ind Electron2016; 63: 7040–7048.
45.
BattinRH. An introduction to the mathematics and methods of astrodynamics, Cleveland, OH: AIAA, 1999.
46.
Wang Q, Zhou B and Duan G. Robust gain scheduled control of spacecraft rendezvous system subject to input saturation. Aerospace Science and Technology 2015; 42: 442–450.
47.
KhargonekarPPNagpalKMPoollaKR. control with transients. SIAM J Control Optim1991; 29: 1373–1393.
48.
Namerikawa T, Fujita M and Smith RS. A generalized control system design attenuating initial state uncertainties. In: Proceedings of the American control conference, Anchorage, AK, USA, 8–10 May 2002, pp.2204–2209.
49.
SavkinAVPathiranaPNFaruqiFA. Problem of precision missile guidance: LQR and control frameworks. IEEE Trans Aerosp Electron Syst2003; 39: 901–910.
50.
FooYK. control with initial conditions. IEEE Trans Circuits Syst2006; 53: 867–871.
51.
ShengDYangXKarimiHR. Robust control for autonomous spacecraft evacuation with model uncertainty and upper bound of performance with constraints. Math Probl Eng2014. Article ID 589381:16 pages.
