Abstract
In this study, two different controllers have been designed to perform the rendezvous and docking tasks of two nonidentical and noncooperative cubic satellites. Firstly, the motion of cubic satellites was modeled with chaotic equations. After selecting suitable chaotic models, fuzzy sliding mode controller (FSMC) and a new intuitionistic fuzzy sliding mode controller (IFSMC), which are applied to synchronization systems under the same initial conditions, have been designed. It has been observed that both synchronizations reach stability by applying the controllers designed by considering the Lyapunov stability criteria. After a while, a short-term and random disturbance was applied to the synchronization systems and the response of both controllers was observed. The numerical results showed that the synchronization system with both controllers was stable, robust, efficient, fast and chattering-free. However, synchronization system with IFSMC was found to be more robust, faster and more efficient than synchronization system with FSMC.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
M. Akram, S. Habib, I. Javed, Intuitionistic fuzzy logic control for washing machines. Indian J. Sci. Technol. 7, 654–661 (2014). https://doi.org/10.17485/ijst/2014/v7i5.20
M. Akram, S. Shahzad, A. Butt, A. Khaliq, Intuitionistic fuzzy logic control for heater fans. Math. Comput. Sci. 7, 367–378 (2013). https://doi.org/10.1007/s11786-013-0161-x
Ö. Atan, F. Kutlu, Synchronization control of two chaotic systems via a novel fuzzy control method, in 2nd International Conference on Pure and Applied Mathematics (2018), p. 51
Ö. Atan, F. Kutlu, O. Castillo, Intuitionistic fuzzy sliding controller for uncertain hyperchaotic synchronization. Int. J. Fuzzy Syst. 22, 1430–1443 (2020). https://doi.org/10.1007/s40815-020-00878-x
K. Atanassov, Intuitionistic Fuzzy Sets (Physica, Heidelberg, 1999)
O. Castillo, Framework for optimization of ıntuitionistic and type-2 fuzzy systems in control applications, in Recent Advances in Intuitionistic Fuzzy Logic Systems (Springer, 2019), pp. 79–86. https://doi.org/10.1007/978-3-030-02155-9_7
O. Castillo, F. Kutlu, Ö. Atan, Intuitionistic fuzzy control of twin rotor multiple input multiple output systems. J. Intell. Fuzzy Syst. 38, 821–833 (2020). https://doi.org/10.3233/JIFS-179451
T. Chaira, Fuzzy Set and Its Extension: The Intuitionistic Fuzzy Set (Wiley, 2019). https://doi.org/10.1002/9781119544203
M. Chegini, H. Sadati, H. Salarieh, Chaos analysis in attitude dynamics of a flexible satellite. Nonlinear Dyn. 93, 1421–1438 (2018). https://doi.org/10.1007/s11071-018-4269-z
M. Chegini, H. Sadati, H. Salarieh, Analytical and numerical study of chaos in spatial attitude dynamics of a satellite in an elliptic orbit. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 233, 561–577 (2018). https://doi.org/10.1177/0954406218762019
H. Delavari, R. Ghaderi, A. Ranjbar, S. Momani, Fuzzy fractional order sliding mode controller for nonlinear systems. Commun. Nonlinear Sci. Numer. Simul. 15, 963–978 (2010). https://doi.org/10.1016/j.cnsns.2009.05.025
K. Dong, J. Luo, Z. Dang, L. Wei, Tube-based robust output feedback model predictive control for autonomous rendezvous and docking with a tumbling target. Adv. Space Res. 65, 1158–1181 (2020). https://doi.org/10.1016/j.asr.2019.11.014
E.D. Dongmo, K.S. Ojo, P. Woafo, A.N. Njah, Difference synchronization of ıdentical and nonidentical chaotic and hyperchaotic systems of different orders using active backstepping design. J. Comput. Nonlinear Dyn. 13 (2018). https://doi.org/10.1115/1.4039626
D. Gao, J. Luo, W. Ma, B. Englot, Parameterized nonlinear suboptimal control for tracking and rendezvous with a non-cooperative target. Aerosp. Sci. Technol. 87, 15–24 (2019). https://doi.org/10.1016/j.ast.2019.01.044
W. Hahn, Stability of Motion (Springer, Berlin, 1967)
P. Hajek, V. Olej, Defuzzification methods in intuitionistic fuzzy inference systems of Takagi-Sugeno type: the case of corporate bankruptcy prediction, in 2014 11th International Conference on Fuzzy Systems and Knowledge Discovery (FKSD) (2014), pp. 232–236. https://doi.org/10.1109/FSKD.2014.6980838
P. Hájek, V. Olej, Adaptive ıntuitionistic fuzzy ınference systems of Takagi-Sugeno type for regression problems, in Artificial Intelligence Applications and Innovations (2012), pp. 206–216. https://doi.org/10.1007/978-3-642-33409-2_22
I. Iancu, M. Gabroveanu, M. Cosulschi, Intuitionistic fuzzy control based on association rules, in Computational Collective Intelligence. Technologies and Applications (2013), pp. 235–244. https://doi.org/10.1007/978-3-642-40495-5_24
W. Jiang, B. Wei, X. Liu, X. Li, H. Zheng, Intuitionistic fuzzy power aggregation operator based on entropy and its application in decision making. Int. J. Intell. Syst. 33, 49–67 (2018). https://doi.org/10.1002/int.21939
A. Khan, S. Kumar, Study of chaos in chaotic satellite systems. Pramana J. Phys. 90, 1–9 (2018). https://doi.org/10.1007/s12043-017-1502-0
A. Khan, S. Kumar, Measuring chaos and synchronization of chaotic satellite systems using sliding mode control. Optim. Control Appl. Methods 39, 1597–1609 (2018). https://doi.org/10.1002/oca.2428
A. Khan, S. Kumar, Analysis and time-delay synchronisation of chaotic satellite systems. Pramana J. Phys. 91, 1–13 (2018). https://doi.org/10.1007/s12043-018-1610-5
C.-L. Kuo, Design of an adaptive fuzzy sliding-mode controller for chaos synchronization. Int. J. Nonlinear Sci. Numer. Simul. 8, 631–636 (2007). https://doi.org/10.1515/IJNSNS.2007.8.4.631
C.L. Kuo, T.H.S. Li, N.R. Guo, Design of a novel fuzzy sliding-mode control for magnetic ball levitation system. J. Intell. Robot. Syst. 42, 295–316 (2005). https://doi.org/10.1007/s10846-004-3026-3
F. Kutlu, Ö. Atan, O. Silahtar, Intuitionistic fuzzy adaptive sliding mode control of nonlinear systems. Soft Comput. 24, 53–64 (2020). https://doi.org/10.1007/s00500-019-04286-8
A. Lassoued, O. Boubaker, Hybrid chaotic synchronisation between identical and non-identical fractional-order systems. Int. J. Comput. Appl. Technol. 60, 134 (2019). https://doi.org/10.1504/IJCAT.2019.100134
K.H. Lee, First Course on Fuzzy Theory and Applications (Springer, 2004). https://doi.org/10.1007/3-540-32366-x
J. Li, Z. Gong, SISO intuitionistic fuzzy systems: IF-t-norm, IF-R-implication, and universal approximators. IEEE Access 7, 70265–70278 (2019). https://doi.org/10.1109/ACCESS.2019.2918169
P. Li, Z.H. Zhu, Model predictive control for spacecraft rendezvous in elliptical orbit. Acta Astron. 146, 339–348 (2018). https://doi.org/10.1016/j.actaastro.2018.03.025
Q. Li, B. Zhang, J. Yuan, H. Wang, Potential function based robust safety control for spacecraft rendezvous and proximity operations under path constraint. Adv. Space Res. 62, 2586–2598 (2018). https://doi.org/10.1016/j.asr.2018.08.003
Y. Lin, X. Zhou, S. Gu, S. Wang, The Takagi-Sugeno ıntuitionistic fuzzy systems are universal approximators, in 2012 2nd International Conference on Consumer Electronics, Communications and Networks (CECNet) (IEEE, 2012), pp. 2214–2217. https://doi.org/10.1109/CECNet.2012.6202025
Y. Liu, Y. Lyu, G. Ma, 6-DOF multi-constrained adaptive tracking control for noncooperative space target. IEEE Access 7, 48739–48752 (2019). https://doi.org/10.1109/ACCESS.2019.2910304
A.M. Long, M.G. Richards, D.E. Hastings, On-orbit servicing: a new value proposition for satellite design and operation. J. Spacecraft Rockets 44, 964–976 (2007). https://doi.org/10.2514/1.27117
M. Marinov, V. Lazarov, Intuitionistic fuzzy robot motion control. Probl. Eng. Cybern. Robot. 69, 40–51 (2018)
M.R. Mufti, H. Afzal, F. Ur-Rehman, W. Aslam, M.I. Qureshi, Transmission projective synchronization of multiple non-identical coupled chaotic systems using sliding mode control. IEEE Access 7, 17847–17861 (2019). https://doi.org/10.1109/ACCESS.2019.2895067
V. Nekoukar, A. Erfanian, Adaptive fuzzy terminal sliding mode control for a class of MIMO uncertain nonlinear systems. Fuzzy Sets Syst. 179, 34–49 (2011). https://doi.org/10.1016/j.fss.2011.05.009
A. Ouannas, G. Grassi, A.T. Azar, A new generalized synchronization scheme to control fractional chaotic systems with non-identical dimensions and different orders. Advances in Intelligent Systems and Computing (Springer, 2020). https://doi.org/10.1007/978-3-030-14118-9_42
J. Pomares, L. Felicetti, J. Pérez, M.R. Emami, Concurrent image-based visual servoing with adaptive zooming for non-cooperative rendezvous maneuvers. Adv. Space Res. 61, 862–878 (2018). https://doi.org/10.1016/j.asr.2017.10.054
L.L. Show, J.C. Juang, Y.W. Jan, An LMI-based nonlinear attitude control approach. IEEE Trans. Control Syst. Technol. 11, 73–83 (2003). https://doi.org/10.1109/TCST.2002.806450
M.J. Sidi, Spacecraft Dynamics and Control: A Practical Engineering Approach (Cambridge University Press, 1997)
S. Singh, A.T. Azar, Q. Zhu, Multi-switching master–slave synchronization of non-identical chaotic systems, in Innovative Techniques and Applications of Modelling, Identification and Control. Lecture Notes in Electrical Engineering, vol. 467 (2018), pp. 321–330. https://doi.org/10.1007/978-981-10-7212-3
S.N. Sivanandam, S. Sumathi, S.N. Deepa, Introduction to Fuzzy Logic Using MATLAB (Springer, Berlin, 2007). https://doi.org/10.1007/978-3-540-35781-0
L. Sun, W. He, C. Sun, Adaptive fuzzy relative pose control of spacecraft during rendezvous and proximity maneuvers. IEEE Trans. Fuzzy Syst. 26, 3440–3451 (2018). https://doi.org/10.1109/TFUZZ.2018.2833028
Z. Sun, Synchronization of fractional-order chaotic systems with non-identical orders, unknown parameters and disturbances via sliding mode control. Chin. J. Phys. 56, 2553–2559 (2018). https://doi.org/10.1016/j.cjph.2018.08.007
A.P.M. Tsui, A.J. Jones, The control of higher dimensional chaos: comparative results for the chaotic satellite attitude control problem. Phys. D Nonlinear Phenom. 135, 41–62 (2000). https://doi.org/10.1016/S0167-2789(99)00114-1
T.-C. Lin, T.-Y. Lee, Chaos synchronization of uncertain fractional-order chaotic systems with time delay based on adaptive fuzzy sliding mode control. IEEE Trans. Fuzzy Syst. 19, 623–635 (2011). https://doi.org/10.1109/TFUZZ.2011.2127482
S. Vaidyanathan, Analysis and synchronization of the hyperchaotic Yujun systems via sliding mode control. Adv. Intell. Syst. Comput. (AISC) 176, 329–337 (2012). https://doi.org/10.1007/978-3-642-31513-8_34
S. Vaidyanathan, S. Sampath, Global chaos synchronization of hyperchaotic Lorenz systems by sliding mode control, in Advances in Digital Image Processing and Information Technology (2011), pp. 156–164. https://doi.org/10.1007/978-3-642-24055-3_16
V.K. Yadav, G. Prasad, M. Srivastava, S. Das, Combination–combination phase synchronization among non-identical fractional order complex chaotic systems via nonlinear control. Int. J. Dyn. Control 7, 330–340 (2019). https://doi.org/10.1007/s40435-018-0432-0
V.K. Yadav, V.K. Shukla, S. Das, A.Y.T. Leung, M. Srivastava, Function projective synchronization of fractional order satellite system and its stability analysis for incommensurate case. Chin. J. Phys. 56, 696–707 (2018). https://doi.org/10.1016/j.cjph.2018.01.008
H.T. Yau, C.L. Chen, Chattering-free fuzzy sliding-mode control strategy for uncertain chaotic systems. Chaos Solitons Fractals 30, 709–718 (2006). https://doi.org/10.1016/j.chaos.2006.03.077
L.A. Zadeh, Fuzzy Sets, Information and Control (1965)
L. Zhang, F. Zhu, Y. Hao, W. Pan, Rectangular-structure-based pose estimation method for non-cooperative rendezvous. Appl. Opt. 57, 6164–6173 (2018). https://doi.org/10.1364/ao.57.006164
R. Zhang, Satellite Orbit Attitude Dynamics and Control (Univ. Aeronaut. Astronaut. Press, Beijing, 1998), p. 115
Y. Zhang, P. Huang, K. Song, Z. Meng, An angles-only navigation and control scheme for noncooperative rendezvous operations. IEEE Trans. Ind. Electron. 66, 8618–8627 (2019). https://doi.org/10.1109/TIE.2018.2884213
B.Z. Zhou, X.F. Liu, G.P. Cai, Motion-planning and pose-tracking based rendezvous and docking with a tumbling target. Adv. Space Res. 65, 1139–1157 (2020). https://doi.org/10.1016/j.asr.2019.11.013
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Silahtar, O., Kutlu, F., Atan, Ö., Castillo, O. (2023). Rendezvous and Docking Control of Satellites Using Chaos Synchronization Method with Intuitionistic Fuzzy Sliding Mode Control. In: Castillo, O., Melin, P. (eds) Fuzzy Logic and Neural Networks for Hybrid Intelligent System Design. Studies in Computational Intelligence, vol 1061. Springer, Cham. https://doi.org/10.1007/978-3-031-22042-5_10
Download citation
DOI: https://doi.org/10.1007/978-3-031-22042-5_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-22041-8
Online ISBN: 978-3-031-22042-5
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)