Distributed Fuzzy Adaptive Sliding Mode Formation for Nonlinear Multi-quadrotor Systems

Document Type : Original Article

Authors

1 Department of Electrical Engineering, Islamic Azad University, Damavand Branch, Tehran, Iran

2 Department of Electrical Engineering, University of Qom, Qom, Iran

3 Department of Aerospace Engineering, Shahid Beheshti University, Tehran, Iran

Abstract

This paper suggests a decentralized adaptive sliding mode formation procedure for affine nonlinear multi-quadrotor under a fixed directed topology wherever the followers are conquered by dynamical uncertainties. Compared with the previous studies which primarily concentrated on linear single-input single-output (SISO) agents or nonlinear agents with constant control gain, the proposed method is applied on affine nonlinear agents with nonlinear control gain such as the quadrotor. This designing procedure overcomes the problem of unknown nonlinear affine functions of the quadrotors. Fuzzy systems are engaged both to compensate recursively the unknown nonlinear functions and to apply the expert’s knowledge on the formation technique. On-line updating the controller parameters, achieving the formation of quadrotor, boundedness of all signals involved in the closed loop of the quadrotor, and chattering reduction are the focal features of the proposed formation methodology. To demonstrate the persistency and efficiency of the methodology, a numerical example of the multi-quadrotor system is considered in this paper.

Keywords


 
1. Ghasemi, R., “Designing observer based variable structure
controller for large scale nonlinear systems”, IAES International
Journal of Artificial Intelligence, Vol. 2, No. 3, (2013), 125–135.  
2. Chen, C.P., Wen, G.X., Liu, Y.J. and Wang, F. Y., “Adaptive
consensus control for a class of nonlinear multiagent time-delay
systems using neural networks”, IEEE Transactions on Neural
Networks and Learning Systems, Vol. 25, No. 6, (2014), 1217–
1226.  
3. Ghasemi, R., “Adaptive state tracking controller for multi-input
multi-output non-affine nonlinear systems”, International
Journal of Computer and Electrical Engineering, Vol. 3, No. 3,
(2011), 426–431.  
4. Chen, C.P., Liu, Y.J. and Wen, G. X., “Fuzzy neural networkbased adaptive control for a class of uncertain nonlinear
stochastic systems”, IEEE Transactions on Cybernetics,Vol.44,No.5,(2013),583–593.

5. Wang, X., Li, T., Chen, C.P. and Lin, B., “Adaptive robust control
based on single neural network approximation for a class of
uncertain strict-feedback discrete-time nonlinear systems”,
Neurocomputing, Vol. 138, (2014), 325–331.  
6. Li, D., Ma, J., Zhu, H. and Sun, M., “The consensus of multi-agent
systems with uncertainties and randomly occurring nonlinearities
via impulsive control”, International Journal of Control,
Automation and Systems, Vol. 14, No. 4, (2016), 1005–1011.  
7. Djaidja, S. and Wu, Q., “Leader-following consensus of singleintegrator
multi-agent systems under noisy and delayed
communication”, International Journal of Control, Automation
and Systems, Vol. 14, No. 2, (2016), 357–366.  
8. Chen, C.P., Ren, C.E. and Du, T., “Fuzzy observed-based
adaptive consensus tracking control for second-order multiagent
systems with heterogeneous nonlinear dynamics”, IEEE
Transactions on Fuzzy Systems, Vol. 24, No. 4, (2015), 906–915.  
9. Chen, C.P., Wen, G.X., Liu, Y.J. and Liu, Z., “Observer-based
adaptive backstepping consensus tracking control for high-order
nonlinear semi-strict-feedback multiagent systems”, IEEE
Transactions on Cybernetics, Vol. 46, No. 7, (2015), 1591–1601.  
10. Shen, Q., Shi, P. and Shi, Y., “Distributed adaptive fuzzy control
for nonlinear multiagent systems via sliding mode observers”,
IEEE Transactions on Cybernetics, Vol. 46, No. 12, (2015),
3086–3097.  
11. Wang, G., Wang, C., Li, L. and Du, Q., “Distributed adaptive
consensus tracking control of higher-order nonlinear strictfeedback
multi-agent systems using neural networks”,
Neurocomputing, Vol. 214, (2016), 269–279.  
12. Wang, T., Zhang, Y., Qiu, J. and Gao, H., “Adaptive fuzzy
backstepping control for a class of nonlinear systems with
sampled and delayed measurements”, IEEE Transactions on 
Fuzzy Systems, Vol. 23, No. 2, (2014), 302–312.  
13. Wang, T., Qiu, J. and Gao, H., “Adaptive neural control of
stochastic nonlinear time-delay systems with multiple
constraints”, IEEE Transactions on Systems, Man, and
Cybernetics: Systems, Vol. 47, No. 8, (2016), 1875–1883.  
14. Wang, T., Qiu, J., Gao, H. and Wang, C., “Network-based fuzzy
control for nonlinear industrial processes with predictive
compensation strategy”, IEEE Transactions on Systems, Man,
and Cybernetics: Systems, Vol. 47, No. 8, (2016), 2137–2147.  
15. Wang, T., Gao, H. and Qiu, J., “A combined fault-tolerant and
predictive control for network-based industrial processes”, IEEE
Transactions on Industrial Electronics, Vol. 63, No. 4, (2016),
2529–2536.  
16. Sanchez, J. and Fierro, R., “Sliding mode control for robot
formations”, In Proceedings of the 2003 IEEE International
Symposium on Intelligent Control, IEEE, (2003), 438–443.  
17. Defoort, M., Floquet, T., Kokosy, A. and Perruquetti, W.,
“Sliding-mode formation control for cooperative autonomous
mobile robots”, IEEE Transactions on Industrial Electronics,
Vol. 55, No. 11, (2008), 3944–3953.  
18. Chang, Y.H., Yang, C.Y., Chan, W.S., Chang, C.W. and Tao, C.
W., “Leader-following formation control of multi-robot systems
with adaptive fuzzy terminal sliding-mode controller”, In 2013
International Conference on System Science and Engineering
(ICSSE), IEEE, (2013), 45–50.  
19. Guillet, A., Lenain, R., Thuilot, B. and Martinet, P., “Adaptable
robot formation control: adaptive and predictive formation control
of autonomous vehicles”, IEEE Robotics & Automation
Magazine, Vol. 21, No. 1, (2014), 28–39.  
20. Shasti, B., Alasty, A. and Assadian, N., “Robust distributed
control of spacecraft formation flying with adaptive network
topology”, Acta Astronautica, Vol. 136, (2017), 281–296.  
21. Ettefagh, M.H., De Doná, J., Naraghi, M. and Towhidkhah, F.,
“Control of Constrained Linear-Time Varying Systems via Kautz
Parametrization of Model Predictive Control Scheme”, Emerging
Science Journal, Vol. 1, No. 2, (2017), 65–74.  
22. Li, J., Wen, G., Gan, J., Zhang, L. and Zhang, S., “Sparse
Nonlinear Feature Selection Algorithm via Local Structure
Learning”, Emerging Science Journal, Vol. 3, No. 2, (2019),
115–129.  
23. Brustad, T. F., “Preliminary Studies on Transition Curve
Geometry: Reality and Virtual Reality”, Emerging Science
Journal, Vol. 4, No. 1, (2020), 1–10.  
24. Espejel-García, D., Ortíz-Anchondo, L.R., Alvarez-Herrera, C.,
Hernandez-López, A., Espejel-García, V.V. and VillalobosAragón,
A., “An alternative vehicle counting tool using the
Kalman filter within MATLAB”, Civil Engineering Journal,
Vol. 3, No. 11, (2017), 1029–1035.  
25. Berdnikov, V. and Lokhin, V., “Synthesis of Guaranteed Stability
Regions of a Nonstationary Nonlinear System with a Fuzzy
Controller”, Civil Engineering Journal, Vol. 5, No. 1, (2019),
107–116.