Abstract
This paper investigates the problem of robust decentralized fault-tolerant resilient control for fractional-order large-scale interconnected uncertain system, and the problem considered here is subject to mixed H∞ and passivity performance constraint, external disturbances, controller perturbations and control input saturation. Based on the Lyapunov approach, the sufficient conditions are derived in terms of linear matrix inequalities to ensure the asymptotic stabilization of the fractional-order large-scale system with a prespecified mixed H∞ and passivity performance index. The main objective of this work is to design a robust decentralized fault-tolerant resilient controller which compensates both actuator fault and input saturation in its design for obtaining the required result. Finally, a numerical example is included to illustrate the effectiveness of the designed control law. The simulation results reveal that our proposed controller not only can effectively deal with actuator faults, but also has very good robustness for input saturation and external disturbances.
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Z. Liao, C. Peng, W. Li, and Y. Wang, “Robust stability analysis for a class of fractional-order systems with uncertain parameters,” Journal of Franklin Institute, vol. 348, no. 6, pp. 1101–1113, August 2011.
Y.-H. Lan and Y. Zhouc, “Non-fragile observer-based robust control for a class of fractional-order nonlinear systems,” Systems and Control Letters, vol. 62, no. 12, pp. 1143–1150, December 2013.
R. Sakthivel, C. K. Ahn, and Maya Joby, “Fault-tolerant resilient control for Fuzzy fractional order systems,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2018. DOI: 10.1109/TSMC.2018.2835442
Q. Wang and D.-L. Qi, “Synchronization for fractional order chaotic systems with uncertain parameters,” International Journal of Control, Automation, and Systems, vol. 14, no. 1, pp. 211–216, February 2016.
S. Marir, M. Chadli and D. Bouagada, “A novel approach of admissibility for singular linear continuous-time fractional-order systems,” International Journal of Control, Automation, and Systems, vol. 15, no. 2, pp. 959–964, April 2017.
N. Liu, J. Fang, W. Deng, Z.-J. Wu, and G.-Q. Ding, “Synchronization for a class of fractional-order linear complex networks via impulsive control,” International Journal of Control, Automation, and Systems, vol. 16, pp. 1–6, October 2018.
Y. Boukal, M. Darouach, M. Zasadzinski, and N.-E. Radhy, “Large-scale fractional-order systems: stability analysis and their decentralised functional observers design,” IET Control Theory and Applications, vol. 12, no. 3, pp. 359–367, January 2018.
J. Zhao, C.-M. Lin, and J. Huang, “Decentralized H ∞ sampled-data control for continuous large-scale networked nonlinear systems,” International Journal of Fuzzy Systems, vol. 19, no. 2, pp. 504–515, February 2016.
Y. Li and J. Li, “Decentralized stabilization of fractional-order T-S fuzzy interconnected systems with multiple time delays,” Journal of Intelligent and Fuzzy Systems, vol. 30, no. 1, pp. 319–331, January 2016.
L.-V. Hien and C.-T. Kinh, “Decentralised stabilisation of positive fractional-order interconnected systems,” IET Control Theory and Applications, vol. 11, no. 14, pp. 2391–2395, September 2017.
H. Liu and H. Yu, “Decentralized state estimation for a large-scale spatially interconnected system,” ISA Transactions, vol. 74, pp. 67–76, March 2018.
S. Tong, B. Huo, and Y. Li, “Observer based Adaptive decentralized fuzzy fault-tolerant control of nonlinear largescale systems with actuator failures,” IEEE Transactions on Fuzzy Systems, vol. 22, no. 1, pp. 1–15, February 2014.
S.-S. Majidabad, H.-D. Shandiz, and A. Hajizadeh, “Decentralized sliding mode control of fractional-order largescale nonlinear systems,” Nonlinear Dynamics, vol. 77, no. 1–2, pp. 119–134, July 2014.
J. Li, J.-G. Lu, and Y.-Q. Chen, “Robust decentralized control of perturbed fractional-order linear interconnected systems,” Computers and Mathematics with Applications, vol. 66, no. 5, pp. 844–859, September 2013.
J. Wang, K. Liang, X. Huang, Z. Wang, and H. Shen, “Dissipative fault-tolerant control for nonlinear singular perturbed systems with Markov jumping parameters based on slow state feedback,” Applied Mathematics and Computation, vol. 328, pp. 247–262, July 2018.
J. Wang, M. Chen, H. Shen, J. H. Park, and Z.-G. Wu, “A Markov jump model approach to reliable event-triggered retarded dynamic output feedback H ∞ control for networked systems,” Nonlinear Analysis: Hybrid Systems, vol. 26, pp. 137–150, November 2017.
M. Chen and G. Tao, “Adaptive fault-tolerant control of uncertain nonlinear large-scale systems with unknown dead zone,” IEEE Transactions on Cybernetics, vol. 46, no. 8, pp. 1851–1862, August 2016.
Y. Li, Z. Ma, and S. Tong, “Adaptive fuzzy output-constrained fault-tolerant control of nonlinear stochastic large-scale systems with actuator faults,” IEEE Transactions on Cybernetics, vol. 47, no. 9, pp. 2362–2376, September 2017.
H. Shen, Y. Men, Z.-G. Wu, J. Cao, and G. Lu, “Network-based quantized control for fuzzy singularly perturbed semi-Markov jump systems and its application,” IEEE Transactions on Circuits and Systems-I: Regular Papers, vol. 66, no. 3, pp. 1130–1140, March 2019.
H. Shen, F. Li, S. Xu, and V. Sreeram, “Slow state variables feedback stabilization for semi-Markov jump systems with singular perturbations,” IEEE Transactions on Automatic Control, vol. 63, no. 8, 2709–2714, August 2018.
H. Shen, F. Li, Z. Wu, Ju H. Park, and V. Sreeram, “Fuzzy-model-based non-fragile control for nonlinear singularly perturbed systems with semi-Markov jump parameters,” IEEE Transactions on Fuzzy Systems, vol. 26, no. 6, 3428–3439, Dec. 2018.
Y.-H. Lim, K.-K. Oh, and H.-S. Ahn, “Stability and stabilization of fractional-order linear systems subject to input saturation,” IEEE Transactions on Automatic Control, vol. 58, no. 4, pp. 1062–1067, April 2013.
Y. Yang, D. Yue, and Y. Xue, “Decentralized adaptive neural output feedback control of a class of large-scale timedelay systems with input saturation,” Journal of Franklin Institute, vol. 352, no. 5, pp. 2129–2151, May 2015.
T. Li, R. Li, and J. Li, “Decentralized adaptive neural control of nonlinear interconnected large-scale systems with unknown time delays and input saturation,” Neurocomputing, vol. 74, no. 14–15, pp. 2277–2283, July 2011.
B. Zhu, M. Suo, Y. Chen, Z. Zhang, and S. Li, “Mixed H ∞ and passivity control for a class of stochastic nonlinear sampled-data systems,” Journal of Franklin Institute, vol. 355, no. 7, pp. 3310–3329, May 2018.
O.-M. Kown and J.-H. Park, “Decentralized guaranteed cost control for uncertain large-scale systems using delayed feedback: LMI optimization approach,” Journal of Optimization Theory and Applications, vol. 129, no. 3, pp. 391–414, June 2006.
R. Sakthivel, Maya Joby, C. Wang, and B. Kaviarasan, “Finite-time fault-tolerant control of neutral systems against actuator saturation and nonlinear actuator faults,” Applied Mathematics and Computation, vol. 332, pp. 425–436, September 2018.
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Recommended by Associate Editor Jun Cheng under the direction of Editor Jessie (Ju H.) Park. The research of Yong-Ki Ma was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education (No. 2018R1D1A1B07049623).
Venkatesan Nithya received her B.Sc., M.Sc., and M.Phil. degrees in Mathematics from Bharathiar University, Coimbatore, Tamil Nadu, in 2001, 2003, and 2005, respectively. She served as a Lecturer in the Department of Mathematics, Vellalar College for Women, Erode, from 2005 to 2008. From 2008 to 2012, she was an Assistant professor at the Department of Mathematics, Tiruppur Kumaran College for Women, Tirupur and from 2012 to 2016, she served as an Assistant Professor in the Department of Mathematics of Angel College of Engineering and Technology, Tirupur. She is currently pursuing a Ph.D. degree in the Department of Applied Mathematics, Bharathiar University, Coimbatore, Tamil Nadu. Her current research interests include dynamical systems and control theory.
Rathinasamy Sakthivel received his B.Sc., M.Sc., M.Phil., and Ph.D. degrees in Mathematics from Bharathiar University, Coimbatore, India, in 1992, 1994, 1996, and 1999, respectively. He served as a Lecturer with the Department of Mathematics, Sri Krishna College of Engineering and Technology, Coimbatore, from 2000 to 2001. From 2001 to 2003, he was a Post-Doctoral Fellow with the Department of Mathematics, Inha University, Incheon, South Korea. He was a Visiting Fellow with Max Planck Institute, Magdeburg, Germany, in 2002. From 2003 to 2005, he was a Japan Society for the Promotion of Science Fellow with the Department of Systems Innovation and Informatics, Kyushu Institute of Technology, Kitakyushu, Japan. He was a Research Professor with the Department of Mathematics, Yonsei University, Seoul, South Korea, till 2006. He was a Post-Doctoral Fellow (Brain Pool Program) with the Department of Mechanical Engineering, Pohang University of Science and Technology, Pohang, South Korea, from 2006 to 2008. He served as an Assistant and Associate professor with the Department of Mathematics, Sungkyunkwan University, Suwon, South Korea from 2008 to 2013. From 2013 to 2016, he was a professor at the department of Mathematics, Sri Ramakrishna Institute of Technology, India. He is currently a Professor with the Department of Applied Mathematics, Bharathiar University, Coimbatore India. He has published over 260 research papers in reputed Science Citation Index journals. His current research interests include systems and control theory, optimization techniques, and nonlinear dynamics. He has been on the Editorial Board of international journals, including the IEEE ACCESS, the Journal of the Franklin Institute, Neurocomputing, Advances in Difference equations and Journal of Electrical Engineering & Technology.
Faris Alzahrani received his B.Sc. degree in mathematics from King Abdulaziz University, Jeddah, Saudi Arabia in 2006, and his Ph.D. degree in mathematics from Cardiff University, Cardiff, United Kingdom in 2014. He is currently an Associate Professor with the Department of Mathematics, King Abdulaziz University. He has authored or co-authored over 30 research papers in reputed international journals. His current research interests include differential equations, control theory and dynamical systems.
Yong-Ki Ma received his M.S. and Ph.D. degrees in Mathematics from Yonsei University, Korea, in 2007 and 2011, respectively. Soon after the completion of his Ph.D. degree, he was a Post-Doctoral Fellow at the Department of Statistics, Seoul National University, Korea from 2011 to 2012. Currently, he is an Associate Professor of Applied Mathematics at Kongju National University, Korea. His research interests include stochastic processes, control theory, and stochastic modeling.
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Nithya, V., Sakthivel, R., Alzahrani, F. et al. Decentralized Fault-tolerant Resilient Control for Fractional-order Interconnected Systems with Input Saturation. Int. J. Control Autom. Syst. 17, 2895–2905 (2019). https://doi.org/10.1007/s12555-018-0865-4
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DOI: https://doi.org/10.1007/s12555-018-0865-4