AN OBSERVER-BASED INTELLIGENT DECENTRALIZED VARIABLE STRUCTURE CONTROLLER FOR NONLINEAR NON-CANONICAL NON-AFFINE LARGE SCALE SYSTEMS

Document Type: Research Paper

Authors

1 DEPARTMENT OF ELECTRICAL ENGINEERING, UNIVERSITY OF QOM, QOM, IRAN

2 DEPARTMENT OF ELECTRICAL ENGINEERING, AMIRKABIR UNIVERSITY OF TECHNOLOGY, TEHRAN, IRAN, AND QIAU’S INCUBATOR CENTER OF TECHNOLOGY UNITS (CENTER OF COGNITIVE SYSTEMS), QAZVIN, IRAN

Abstract

In this paper, an observer based fuzzy adaptive controller (FAC) is designed for
a class of large scale systems with non-canonical non-affine nonlinear subsystems. It is
assumed that functions of the subsystems and the interactions among subsystems are
unknown. By constructing a new class of state observer for each follower, the proposed
consensus control method solves the problem of unmeasured states of nonlinear noncanonical
non-affine subsystems. The main characteristics of the proposed observer-based
intelligent controller are: 1) on-line adaptation of the controller and the observer parameters,
2) ultimate boundedness of both the output and the observer errors, 3) boundedness of all
signals involved, 4) employing experts’ knowledge in the controller design procedure and 5)
chattering avoidance. The simulation results are further carried out to demonstrate better the
effectiveness of the proposed fuzzy based consensus controller method.

Keywords


[1] C.C. Cheng, S.H. Chien, Adaptive Sliding Mode Controller Design Based On T–S Fuzzy System Models,
Elsevier Science, Automatica, 42 (2006), 1005-1010.
[2] L. Chen, G. Chen, Y.W. Lee, Fuzzy Modeling And Adaptive Control Of Uncertain Chaotic Systems,
Elsevier Science, Information Sciences, 121 (1999), 27-37.
[3] C.C. Chiang, Adaptive Fuzzy Sliding Mode Control For Time-Delay Uncertain Large-Scale Systems,
Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control
Conference, pp. 4077-4082,Seville, Spain, December, (2005), 12-15.
[4] C. L. P. Chen, G. X. Wen, Y. J. Liu, Adaptive Consensus Control for a Class of Nonlinear Multiagent
Time-Delay Systems Using Neural Networks, IEEE Transaction of neural network learning systems, 25
(2014), 1217-1226.
[5] C. L. P. Chen, Y. J. Liu, G. X. Wen, Fuzzy neural network-based adaptive control for a class of
uncertain nonlinear stochastic systems, IEEE Trans. Cybernetics, 44 (2014), 583-593.
[6] G. Feng, S.G. Cao, N.W. Rees, Stable Adaptive Control Of Fuzzy Dynamic Systems, Elsevier Science,
Fuzzy Sets and Systems, 131 (2002), 217 – 224.
[7] G. Feng, An Approach To Adaptive Control Of Fuzzy Dynamic Systems, IEEE TRANSACTIONS ON
FUZZY SYSTEMS, 10 (2002), 268-275.
[8] R. Ghasemi, M.B. Menhaj, A. Afshar, A decentralized stable fuzzy adaptive controller for large scale
nonlinear systems, Journal of Applied Science, 9 (2009), 892-900.
[9] R. Ghasemi, M.B. Menhaj and A. Afshar, A New Decentralized Fuzzy Model Reference Adaptive
Controller for a Class of Large-scale Non-affine Nonlinear Systems, European Journal of Control, 5
(2009), 1–11.
[10] R Ghasemi, MB Menhaj, A variable structure observer based control design for a class of large scale
MIMO nonlinear systems, Amirkabir International Journal of Modeling, Identification, Simulation &
Control, 48 (2016), 47-56.

[11] N. Golea, A. Golea, K. Benmahammed, Stable Indirect Fuzzy Adaptive Control, Elsevier Science,
Fuzzy Sets and Systems, 137 (2003), 353-366.
[12] A. Hamzaoui, N. Essounbouli, K. Benmahammed, and J. Zaytoon, State Observer Based Robust
Adaptive Fuzzy Controller for Nonlinear Uncertain and Perturbed Systems, IEEE TRANSACTIONS
ON SYSTEMS, MAN, AND CYBERNETICS—PART B, 34 (2004), 23-28.
[13] H.F. Ho, Y.K. Wong, A.B. Rad, W.L. Lo, State Observer Based Indirect Adaptive Fuzzy Tracking
Control, Simulation Modeling Practice and Theory, 13 (2005), 646–663.
[14] Y.C. Hsu, G. Chen, S. Tong, H.X. Li, Integrated Fuzzy Modeling And Adaptive Control For Nonlinear
Systems, Elsevier Science, Information Sciences, 153 (2003), 217-236.
[15] J. Hu, Y. Hong, Leader-following coordination of multiagent systems with coupling time delays,
Physica A, 374 (2007), 853-863.
[16] S. Jagannathan, Adaptive Fuzzy logic control of feedback linearization discrete time dynamical systems
under persistence of excitation, Automatica, 34 (1998), 1295-1310.
[17] X. Jiang,W. Xu, Q.L. Han, Observer-based fuzzy control design with adaptation to delay parameter for
time-delay systems, Elsevier Science, Fuzzy Sets and Systems, 152 (2005), 637–649.
[18] S. Labiod, M. S. Boucherit, T. M. Guerra, Adaptive fuzzy control of a class of MIMO nonlinear
systems, Elsevier Science, Fuzzy Sets and Systems, 151 (2005), 59–77.
[19] S. Labiod, T. M. Guerra, Adaptive fuzzy control of a class of SISO non-affine nonlinear systems,
Elsevier Science, Fuzzy Sets and Systems, 158 (2007), 1126 –1137.
[20] Z. Li, X. Liu, P. Lin, W. Ren, Consensus of linear multi-agent systems with reduced-order observerbased
protocols, Systems & Control Letters, 60- 7 (2011), 510-516.
[21] Y.J. Liu, W. Wang, Adaptive fuzzy control for a class of uncertain non-affine nonlinear systems,
Elsevier Science, Information Sciences, 4 (2007), 1-17.
[22] Y. J. Liu, S. C. Tong, C. L. P. Chen, Adaptive fuzzy control via observer design for uncertain
nonlinear systems with unmodeled dynamics, IEEE Trans. Fuzzy Syst., 21 (2013), 275-288.
[23] Y. J. Liu, S. C. Tong, D. Wang, T. S. Li, C. L. P. Chen, Adaptive neural output feedback controller
design with reduced-order observer for a class of uncertain nonlinear SISO systems, IEEE Trans.
Neural Netw., 22 (2011), 1328-1334.
[24] R. Olfati-Saber, R. M. Murray, Consensus problems in networks of agents with switching topology
and timedelays, IEEE Trans. Automatic Control, 49 (2004), 1520-1533.
[25] C.W. Park, M. Park, Adaptive Parameter Estimator Based On T–S Fuzzy Models And Its Applications
To indirect adaptive fuzzy control design, Elsevier science, Information Sciences, 159 (2004), 125-139.
[26] K. Peng, Y. Yang, Leader-following consensus problem with a varying-velocity leader and timevarying
delays, Physica A, 388 (2009), 193-208.
[27] W. Ren, K. Moore, Y. Chen, High-Order Consensus Algorithms in Cooperative Vehicle Systems, in
Proc. ICNSC, 129 (2006), 457 - 462.
[28] T. Shaocheng, C. Bin, W. Yongfu, fuzzy adaptive output feedback control for MIMO nonlinear
systems, Elsevier Science, Fuzzy Sets and Systems, 156 (2005), 285–299.
[29] Y. Tang, N. Zhang, Y. Li, stable fuzzy adaptive control for a class of nonlinear systems, Elsevier
Science, Fuzzy Sets and Systems, 104 (1999), 279-288.
[30] S. C. Tong, Q. Li, T. Chai, fuzzy adaptive control for a class of nonlinear systems, Elsevier Science,
Fuzzy Sets and Systems, 101 (1999), 31-39.
[31] S. Tong, H.X. Li, W. Wang, Observer-Based Adaptive Fuzzy Control For SISO Nonlinear Systems,
Elsevier Science, Fuzzy Sets and Systems, 148 (2004), 355–376.
[32] S. Tong, H.X. Li, and G. Chen, adaptive fuzzy decentralized control for a class of large-scale
nonlinear systems, IEEE Transactions on Systems, Man, and Cybernetics—Part B, 34 (2004), 24-27.
[33] S. C. Tong, Y. Li, Y. M. Li, and Y. J. Liu, Observerbased adaptive fuzzy backstepping control for a
class of stochastic nonlinear strict-feedback systems, IEEE Trans. Syst., Man, Cybern. Part B, 41
(2011), 1693-1704.
[34] S. C. Tong, Y. M. Li, G. Feng, and T. S. Li, Observer based adaptive fuzzy backstepping dynamic
surface control for a class of MIMO nonlinear systems, IEEE Trans. Syst., Man, Cybern. Part B, 41
(2011), 1124- 1135.
[35] S.Tong and J.Tang and T. Wang, Fuzzy Adaptive Control Of Multivariable Nonlinear Systems,
Elsevier Science, Fuzzy Sets and Systems, 111 (2000), 153-167.
[36] D. Vélez-Díaz and Y. Tang, Adaptive robust fuzzy control of nonlinear systems, IEEE Transactions On
Systems, Man, And Cybernetics—Part B: Cybernetics, 34 (2004), 34-39.

[37] R.J. Wai, M. Kuo, and J.D. Lee, Cascade direct adaptive fuzzy control design for a nonlinear two-axis
inverted-pendulum servomechanism, IEEE Transactions On Systems, Man, and Cybernetics—Part B:
Cybernetics, 38 (2008), 67-77.
[38] X. Wang, T. Li, C. L. P. Chen, Adaptive robust control based on single neural network approximation
for a class of uncertain strict-feedback discrete-time nonlinear systems, Neurocomputing, 138 (2014),
325-331.
[39] H. Wu, Decentralized adaptive robust control for a class of large-scale systems including delayed
state perturbations in the interconnections, IEEE Transactions On Automatic Control, 47 (2002), 1745-
1751.
[40] P. Ying-guo, Z. Hua-guang, Design of fuzzy direct adaptive controller and stability analysis for a
class of nonlinear system, Proceedings of the American Control conference, Philadelphia, Pennsylvania,
(1998), 2274-2275.
[41] T. Yiqian, W. Jianhui, G. Shusheng, Q. Fengying, Fuzzy Adaptive Output Feedback Control For
Nonlinear MIMO Systems Based On Observer, Proceedings of the 5th World Congress on Intelligent
Control and Automation Hangzhou, P.R. China, (2004), 506-510.
[42] W.S. Yu, Model Reference Fuzzy adaptive control for uncertain dynamical systems with time delays,
IEEE International Conference on Systems, Man and Cybernetics, 5 (2004), 5246-5251.
[43] L. Zhang, Stable Fuzzy Adaptive Control Based On Optimal Fuzzy Reasoning, IEEE, Proceedings of
the Sixth International Conference on Intelligent Systems Design and Applications (ISDA'06), (2006),
201-206.
[44] H. Zhang and Z.Bien, Adaptive fuzzy control of MIMO nonlinear systems, Fuzzy Sets and Systems,
115 (2000), 191-204.
[45] H. W. Zhang and F. L. Lewis, Adaptive cooperative tracking control of higher-order nonlinear
systems with unknown dynamics, Automatica, 48 (2012), 1432-1439.
[46] W. Zhu and D. Cheng, Leader-following consensus of second-order agents with multiple time-varying
delays, Automatica, 46 (2010), 1994-1999.