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Volume 5 Issue 1
Jan.  2018

IEEE/CAA Journal of Automatica Sinica

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Ranjith Ravindranathan Nair and Laxmidhar Behera, "Robust Adaptive Gain Higher Order Sliding Mode Observer Based Control-constrained Nonlinear Model Predictive Control for Spacecraft Formation Flying," IEEE/CAA J. Autom. Sinica, vol. 5, no. 1, pp. 367-381, Jan. 2018. doi: 10.1109/JAS.2016.7510253
Citation: Ranjith Ravindranathan Nair and Laxmidhar Behera, "Robust Adaptive Gain Higher Order Sliding Mode Observer Based Control-constrained Nonlinear Model Predictive Control for Spacecraft Formation Flying," IEEE/CAA J. Autom. Sinica, vol. 5, no. 1, pp. 367-381, Jan. 2018. doi: 10.1109/JAS.2016.7510253

Robust Adaptive Gain Higher Order Sliding Mode Observer Based Control-constrained Nonlinear Model Predictive Control for Spacecraft Formation Flying

doi: 10.1109/JAS.2016.7510253
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  • This work deals with the development of a decentralized optimal control algorithm, along with a robust observer, for the relative motion control of spacecraft in leader-follower based formation. An adaptive gain higher order sliding mode observer has been proposed to estimate the velocity as well as unmeasured disturbances from the noisy position measurements. A differentiator structure containing the Lipschitz constant and Lebesgue measurable control input, is utilized for obtaining the estimates. Adaptive tuning algorithms are derived based on Lyapunov stability theory, for updating the observer gains, which will give enough flexibility in the choice of initial estimates. Moreover, it may help to cope with unexpected state jerks. The trajectory tracking problem is formulated as a finite horizon optimal control problem, which is solved online. The control constraints are incorporated by using a nonquadratic performance functional. An adaptive update law has been derived for tuning the step size in the optimization algorithm, which may help to improve the convergence speed. Moreover, it is an attractive alternative to the heuristic choice of step size for diverse operating conditions. The disturbance as well as state estimates from the higher order sliding mode observer are utilized by the plant output prediction model, which will improve the overall performance of the controller. The nonlinear dynamics defined in leader fixed Euler-Hill frame has been considered for the present work and the reference trajectories are generated using Hill-Clohessy-Wiltshire equations of unperturbed motion. The simulation results based on rigorous perturbation analysis are presented to confirm the robustness of the proposed approach.

     

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  • [1]
    D. P. Scharf, F. Y. Hadaegh, and S. R. Ploen, "A survey of spacecraft formation flying guidance and control. Part Ⅱ: control, " in Proc. 2004 American Control Conf., Boston, Massachusetts, 2004, pp. 2976-2985. doi: 10.1109/ACC.2003.1239845
    [2]
    X. Liu and K. D. Kumar, "Network-based tracking control of spacecraft formation flying with communication delays, " IEEE Trans. Aerosp. Electronic Syst., vol. 48, no. 3, pp. 2302-2314, Jul. 2012. http://ieeexplore.ieee.org/xpls/icp.jsp?arnumber=6237593
    [3]
    L. Hui and J. F. Li, "Terminal sliding mode control for spacecraft formation flying, " IEEE Trans. Aerosp. Electronic Syst. vol. 45, no. 3, pp. 835-846, Jul. 2009. http://ieeexplore.ieee.org/xpls/icp.jsp?arnumber=5259168
    [4]
    R. R. Nair and L. Behera, "Swarm aggregation using artificial potential field and fuzzy sliding mode control with adaptive tuning technique, " in Proc. 2012 American Control Conf. , Montreal, Canada, 2012, pp. 6184-6189. doi: 10.1109/ACC.2012.6315463
    [5]
    T. E. Massey and Y. B. Shtessel, "Continuous traditional and highorder sliding modes for satellite formation control, " J. Guid. Control Dynamics, vol. 28, no. 4, pp. 826-831, Jul-Aug. 2005. doi: 10.2514/1.14126
    [6]
    R. R. Nair, L. Behera, V. Kumar, and M. Jamshidi, "Multisatellite formation control for remote sensing applications using artificial potential field and adaptive fuzzy sliding mode control, " IEEE Syst. J., vol. 9, no. 2, pp. 508-518, Jun. 2015. http://ieeexplore.ieee.org/document/6872543/
    [7]
    M. S. de Queiroz, V. Kapila, and Q. G. Yan, "Adaptive nonlinear control of multiple spacecraft formation flying, " J. Guid. Control Dynamics, vol. 23, no. 3, pp. 385-390, May 2000. doi: 10.2514/2.4549?mi=8ed1op&af=R&contents=articlesChapters&countTerms=true&field1=Contrib&target=default&text1=Yan%2C+Q
    [8]
    X. W. Dong, B. C. Yu, Z. Y. Shi, and Y. S. Zhong, "Time-varying formation control for unmanned aerial vehicles: theories and applications, " IEEE Trans. Control Syst. Technol., vol. 23, no. 1, pp. 340-348, Jan. 2015. doi: 10.1109/TCST.2014.2314460
    [9]
    X. W. Dong, Y. Zhou, Z. Ren, and Y. S. Zhong, "Time-varying formation control for unmanned aerial vehicles with switching interaction topologies, " Control Eng. Pract., vol. 46, pp. 26-36, Jan. 2016. http://ieeexplore.ieee.org/document/6842376/
    [10]
    L. Ma, H. B. Min, S. C. Wang, Y. Liu, and S. Y. Liao, "An overview of research in distributed attitude coordination control, " IEEE/CAA J. of Autom. Sinica, vol. 2, no. 2, pp. 121-133, Apr. 2015. http://trj-dd.sagepub.com/lp/institute-of-electrical-and-electronics-engineers/an-overview-of-research-in-distributed-attitude-coordination-control-cftXMMUS0N
    [11]
    Y. Ulybyshev, "Long-term formation keeping of satellite constellation using linear-quadratic controller, " J. Guid. Control Dynamics, vol. 21, no. 1, pp. 109-115, Jan. -Feb. 1998. doi: 10.2514/2.4204
    [12]
    S. B. McCamish, M. Romano, and X. P. Yun, "Autonomous distributed control of simultaneous multiple spacecraft proximity maneuvers, " IEEE Trans. Automat. Sci. Eng., vol. 7, no. 3, pp. 630-644, Jul. 2010. http://ieeexplore.ieee.org/document/5427004/
    [13]
    E. Camponogara and H. F. Scherer, "Distributed optimization for model predictive control of linear dynamic networks with control-input and output constraints, " IEEE Trans. Automat. Sci. Eng., vol. 8, no. 1, pp. 233-242, Jan. 2011. doi: 10.1109/TASE.2010.2061842
    [14]
    X. H. Xia and J. F. Zhang, "Operation efficiency optimisation modelling and application of model predictive control, " IEEE/CAA J. of Autom. Sinica, vol. 2, no. 2, pp. 166-172, Apr. 2015. http://ieeexplore.ieee.org/document/7081656/
    [15]
    L. Breger, J. P. How, and A. Richards, "Model predictive control of spacecraft formations with sensing noise, " in Proc. 2005 American Control Conf., Portland, OR, USA, 2005, pp. 2385-2390. doi: 10.1109%2fACC.2005.1470323
    [16]
    G. J. Sutton and R. R. Bitmead, "Performance and computational implementation of nonlinear model predictive control on a submarine, " in Nonlinear Model Predictive Control, F. Allgöower and A. Zheng, Eds., Birkhäuser Basel, 2000, pp. 461-471. http://www.springerlink.com/content/u221w22737k0240p
    [17]
    J. Shin and H. J. Kim, "Nonlinear model predictive formation flight, " IEEE Trans. Syst. Man Cybernet. -A: Syst. Humans, vol. 39, no. 5, pp. 1116-1125, Sep. 2009. doi: 10.1109/TSMCA.2009.2021935
    [18]
    K. R. Muske and T. A. Badgwell, "Disturbance modeling for offset-free linear model predictive control, " J. Process Control, vol. 12, no. 5, pp. 617-632, Aug. 2002. http://www.sciencedirect.com/science/article/pii/S0959152401000518
    [19]
    A. Levant, "Higher-order sliding modes, differentiation and outputfeedback control, " Int. J. Control, vol. 76, no. 9-10, pp. 924-941, Sept. 2003. doi: 10.1080/0020717031000099029
    [20]
    A. Benallegue, A. Mokhtari, and L. Fridman, "High-order sliding-mode observer for a quadrotor UAV, " Int. J. Robust Nonlin. Control, vol. 18, no. 4-5, pp. 427-440, Mar. 2008. http://www.ams.org/mathscinet-getitem?mr=2392132
    [21]
    A. Levant, "Robust exact differentiation via sliding mode technique, " Automatica, vol. 34, no. 3, pp. 379-384, Mar. 1998. http://dl.acm.org/citation.cfm?id=289304
    [22]
    R. Sharma and M. Aldeen, "Fault and disturbance reconstruction in non-linear systems using a network of interconnected sliding mode observers, " IET Control Theory Appl., vol. 5, no. 6, pp. 751-763, Apr. 2011. http://www.ams.org/mathscinet-getitem?mr=2839661
    [23]
    P. P. Menon and C. Edwards, "An observer based distributed controller for formation flying of satellites, " in Proc. 2011 American Control Conf., San Francisco, CA, USA, 2011, pp. 196-201. http://ieeexplore.ieee.org/xpls/icp.jsp?arnumber=5990884
    [24]
    L. Fridman, Y. Shtessel, C. Edwards, and X. -G. Yan, "Higher-order sliding-mode observer for state estimation and input reconstruction in nonlinear systems, " Int. J. Robust Nonlin. Control, vol. 18, no. 4-5, pp. 399-412, Mar. 2008. doi: 10.1002/rnc.1198
    [25]
    S. Iqbal, C. Edwards, and A. I. Bhatti, "Robust feedback linearization using higher order sliding mode observer, " in Proc. 50th IEEE Conf. Decision and Control and European Control Conf. (CDC-ECC), Orlando, FL, USA, 2011, pp. 7968-7973. http://ieeexplore.ieee.org/xpls/icp.jsp?arnumber=6161097
    [26]
    C. X. Mu, Q. Zong, B. L. Tian, and W. Xu, "Continuous sliding mode controller with disturbance observer for hypersonic vehicles, " IEEE/CAA J. of Autom. Sinica, vol. 2, no. 1, pp. 45-55, Jan. 2015. http://ieeexplore.ieee.org/document/7032905/
    [27]
    A. Heydari and S. N. Balakrishnan, "Finite-horizon control-constrained nonlinear optimal control using single network adaptive critics, " IEEE Trans. Neural Netw. Learning Syst., vol. 24, no. 1, pp. 145-157, Jan. 2013. http://www.ncbi.nlm.nih.gov/pubmed/24808214
    [28]
    N. Boizot, E. Busvelle, and J. -P. Gauthier, "An adaptive high-gain observer for nonlinear systems, " Automatica, vol. 46, no. 9, pp. 1483-1488, Sep. 2010. http://www.sciencedirect.com/science/article/pii/S0005109810002542
    [29]
    Q. X. Lan, J. Yang, S. H. Li, and H. B. Sun, "Finite-time control for 6dof spacecraft formation flying systems, " J. Aerosp. Eng., vol. 28, no. 5, Article no. 04014137, Sep. 2015. doi: 10.1061/(ASCE)AS.1943-5525.0000476
    [30]
    A. Isidori, Nonlinear Control Systems (Third edition). Springer: Berlin, 1995.
    [31]
    A. F. Filippov, Differential Equations with Discontinuous Righthand Sides. Dordrecht: Kluwer Academic, 1988. http://www.ams.org/mathscinet-getitem?mr=114016
    [32]
    J. -J. Slotine and W. P. Li, Applied Nonlinear Control. Englewood Cliffs, NJ: Prentice-Hall, 1991.
    [33]
    S. P. Bhat and D. S. Bernstein, "Geometric homogeneity with applications to finite-time stability, " Math. Control Signals Syst., vol. 17, no. 2, pp. 101-127, Jun. 2005. doi: 10.1007/s00498-005-0151-x
    [34]
    A. Levant, "Homogeneity approach to high-order sliding mode design, " Automatica, vol. 41, no. 5, pp. 823-830, May 2005. http://www.ams.org/mathscinet-getitem?mr=2157713
    [35]
    Y. Orlov, "Finite time stability and robust control synthesis of uncertain switched systems, " SIAM J. Control Optim., vol. 43, no. 4, pp. 1253-1271, Apr. 2004. http://dl.acm.org/citation.cfm?id=1042014
    [36]
    K. T. Alfriend, S. R. Vadali, P. Gurfil, J. P. How, and L. S. Breger, Spacecraft Formation Flying: Dynamics, Control and Navigation. Amsterdam: Elsevier, 2010. http://www.researchgate.net/publication/259740969_Spacecraft_formation_flying_dynamics_control_and_navigation
    [37]
    D. Vallado, Fundamentals of Astrodynamics and Applications (Second edition). New York: Springer, 2001. doi: 10.2514/2.4291

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