Research Paper:
Predictive Controller for Large-Scale Fuzzy Polynomial Systems
Ziqin Xu and Lizhen Li
Shanghai University of Electric Power
No.1851 Huchenghuan Road, Pudong New Area, Shanghai 201306, China
Corresponding author
This paper presents an innovative method to tackle the predictive-control challenges associated with large-scale fuzzy polynomial systems comprising interconnected polynomial fuzzy systems. This study models large-scale nonlinear fuzzy systems in a polynomial framework, which can reduce the number of fuzzy rules. We derive the conditions for controller synthesis in the main theorem using the Lyapunov theory and sum-of-squares technique. Simulation results confirm the validity and efficiency of this approach.
- [1] W.-J. Wang and L.-G. Mau, “Stabilization and estimation for perturbed discrete time-delay large-scale systems,” IEEE Trans. on Automatic Control, Vol.42, No.9, pp. 1277-1282, 1997. https://doi.org/10.1109/9.623092
- [2] M. Chen and G. Tao, “Adaptive fault-tolerant control of uncertain nonlinear large-scale systems with unknown dead zone,” IEEE Trans. on Cybernetics, Vol.46, No.8, pp. 1851-1862, 2016. https://doi.org/10.1109/TCYB.2015.2456028
- [3] H. Yang, Y. Wang, and Y. Yang, “Adaptive control for large-scale nonlinear systems with time delays and unmodeled dynamics,” IEEE Access, Vol,5, pp. 938-945, 2017. https://doi.org/10.1109/ACCESS.2016.2622281
- [4] D. Zhang, S. K. Nguang, and L. Yu, “Distributed control of large-scale networked control systems with communication constraints and topology switching,” IEEE Trans. on Systems, Man, and Cybernetics: Systems, Vol.47, No.7, pp. 1746-1757, 2017. https://doi.org/10.1109/TSMC.2017.2681702
- [5] K. Sun, S. Sui, and S. Tong, “Fuzzy adaptive decentralized optimal control for strict feedback nonlinear large-scale systems,” IEEE Trans. on Cybernetics, Vol.48, No.4, pp. 1326-1339, 2018. https://doi.org/10.1109/TCYB.2017.2692384
- [6] V. Lakshmikantham, “Large-scale dynamic systems: Stability and structure [book reviews],” IEEE Trans. on Automatic Control, Vol.26, No.4, pp. 976-977, 1981. https://doi.org/10.1109/TAC.1981.1102729
- [7] A. Zecevic and D. D. Siljak, “Control of Complex Systems: Structural Constraints and Uncertainty,” Springer, 2010. https://doi.org/10.1007/978-1-4419-1216-9
- [8] J. Lunze, “Feedback Control of Large-Scale Systems,” Prentice Hall, 1992.
- [9] Z. Hu, “Decentralized stabilization of large scale interconnected systems with delays,” IEEE Trans. on Automatic Control, Vol.39, No.1, pp. 180-182, 1994. https://doi.org/10.1109/9.273363
- [10] R.-J. Wang, W.-W. Lin, and W.-J. Wang, “Stabilizability of linear quadratic state feedback for uncertain fuzzy time-delay systems,” IEEE Trans. on Systems, Man, and Cybernetics, Part B (Cybernetics), Vol.34, No.2, pp. 1288-1292, 2004. https://doi.org/10.1109/TSMCB.2003.818437
- [11] W.-J. Wang and C.-H. Sun, “A relaxed stability criterion for T-S fuzzy discrete systems,” IEEE Trans. on Systems, Man, and Cybernetics, Part B (Cybernetics), Vol.34, No.5, pp. 2155-2158, 2004. https://doi.org/10.1109/TSMCB.2004.833332
- [12] P. Baranyi et al., “SVD-based complexity reduction to TS fuzzy models,” IEEE Trans. on Industrial Electronics, Vol.49, No.2, pp. 433-443, 2002. https://doi.org/10.1109/41.993277
- [13] F. Delmotte, T. M. Guerra, and M. Ksantini, “Continuous Takagi–Sugeno’s models: Reduction of the number of LMI conditions in various fuzzy control design technics,” IEEE Trans. on Fuzzy Systems, Vol.15, No.3, pp. 426-438, 2007. https://doi.org/10.1109/TFUZZ.2006.889829
- [14] H. H. Choi, “LMI-based nonlinear fuzzy observer-controller design for uncertain MIMO nonlinear systems,” IEEE Trans. on Fuzzy Systems, Vol.15, No.5, pp. 956-971, 2007. https://doi.org/10.1109/TFUZZ.2006.890676
- [15] K. Tanaka, H. Yoshida, H. Ohtake, and H. O. Wang, “A sum-of-squares approach to modeling and control of nonlinear dynamical systems with polynomial fuzzy systems,” IEEE Trans. on Fuzzy Systems, Vol.17, No.4, pp. 911-922, 2008. https://doi.org/10.1109/TFUZZ.2008.924341
- [16] K. Tanaka, H. Ohtake, T. Seo, M. Tanaka, and H. O. Wang, “Polynomial fuzzy observer designs: A sum-of-squares approach,” IEEE Trans. on Systems, Man, and Cybernetics, Part B (Cybernetics), Vol.42, No.5, pp. 1330-1342, 2012. https://doi.org/10.1109/TSMCB.2012.2190277
- [17] S.-H. Han, V.-P. Vu, and M.-S. Tran, “Decentralized polynomial observer design for discrete-time large-scale polynomial T-S fuzzy system,” Mathematical Problems in Engineering, Vol.2019, Article No.2192768, 2019. https://doi.org/10.1155/2019/2192768
- [18] Z. Feng, Y. Yang, and H.-K. Lam, “New results on sliding mode control for polynomial fuzzy singular systems with time-varying delay,” Int. J. of Robust and Nonlinear Control, Vol.33, No.4, pp. 2779-2795, 2023. https://doi.org/10.1002/rnc.6543
- [19] R. Chaibi, M. Yagoubi, and R. El Bachtiri, “Robust DOF control for uncertain polynomial fuzzy systems in finite frequency domain,” Results in Control and Optimization, Vol.5, Article No.100062, 2021. https://doi.org/10.1016/j.rico.2021.100062
- [20] B. Pang and Q. Zhang, “Observer-based passive control for polynomial fuzzy singular systems with time-delay via sliding mode control,” Nonlinear Analysis: Hybrid Systems, Vol.37, Article No.100909, 2020. https://doi.org/10.1016/j.nahs.2020.100909
- [21] H. Yaghoubi, A. Zare, and R. Alizadehsani, “Analysis and design of robust controller for polynomial fractional differential systems using sum of squares,” Axioms, Vol.11, No.11, Article No.623, 2022. https://doi.org/10.3390/axioms11110623
- [22] E. August and A. Papachristodoulou, “Feedback control design using sum of squares optimisation,” European J. of Control, Vol.68, Article No.100683, 2022. https://doi.org/10.1016/j.ejcon.2022.100683
- [23] G. B. Koo, “Observer-based decentralized fuzzy control for discrete-time nonlinear large-scale systems,” Int. J. of Control, Automation and Systems, Vol.21, No.5, pp. 1670-1681, 2023. https://doi.org/10.1007/s12555-022-0303-5
- [24] M. H. Khooban, N. Vafamand, T. Niknam, T. Dragicevic, and F. Blaabjerg, “Model-predictive control based on Takagi-Sugeno fuzzy model for electrical vehicles delayed model,” IET Electric Power Applications, Vol.11, No.5, pp. 918-934, 2017. https://doi.org/10.1049/iet-epa.2016.0508
- [25] M. Sarbaz, I. Zamani, M. Manthouri, and A. Ibeas, “Decentralized robust interval type-2 fuzzy model predictive control for Takagi–Sugeno large-scale systems,” Automatika, Vol.63, No.1, pp. 49-63, 2022. https://doi.org/10.1080/00051144.2021.2003113
- [26] H. J. Kim, J. B. Park, and Y. H. Joo, “Decentralized H∞ fuzzy filter for nonlinear large-scale sampled-data systems with uncertain interconnections,” Fuzzy Sets and Systems, Vol.344, pp. 145-162, 2018. https://doi.org/10.1016/j.fss.2017.10.010
- [27] I. Boulkaibet, K. Belarbi, S. Bououden, T. Marwala, and M. Chadli, “A new T-S fuzzy model predictive control for nonlinear processes,” Expert Systems with Applications, Vol.88, pp. 132-151, 2017. https://doi.org/10.1016/j.eswa.2017.06.039
- [28] L. Wei et al., “T-S fuzzy model predictive control for vehicle yaw stability in nonlinear region,” IEEE Trans. on Vehicular Technology, Vol.70, No.8, pp. 7536-7546, 2021. https://doi.org/10.1109/TVT.2021.3091809
- [29] H. Wang and G.-H. Yang, “Decentralized fault detection for affine T–S fuzzy large-scale systems with quantized measurements,” IEEE Trans. on Fuzzy Systems, Vol.26, No.3, pp. 1414-1426, 2018. https://doi.org/10.1109/TFUZZ.2017.2724019
- [30] Q. Wang, Y. Pan, J. Cao, and H. Liu, “Adaptive fuzzy echo state network control of fractional-order large-scale nonlinear systems with time-varying deferred constraints,” IEEE Trans. on Fuzzy Systems, Vol.32, No.2, pp. 634-648, 2024. https://doi.org/10.1109/TFUZZ.2023.3305606
- [31] S. Prajna, A. Papachristodoulou, and F. Wu, “Nonlinear control synthesis by sum of squares optimization: A Lyapunov-based approach,” 2004 5th Asian Control Conf., Vol.1, pp. 157-165, 2004.
- [32] T. Wang, S. Tong, and Y. Li, “Robust adaptive decentralized fuzzy control for stochastic large-scale nonlinear systems with dynamical uncertainties,” Neurocomputing, Vol.97, pp. 33-43, 2012. https://doi.org/10.1016/j.neucom.2012.05.017
- [33] S. Prajna, A. Papachristodoulou, P. Seiler, and P. A. Parrilo, “SOSTOOLS – Sum of squares optimization toolbox for MATLAB, Version 2.00,” 2004.
- [34] W. Chang and W.-J. Wang, “H∞ fuzzy control synthesis for a large-scale system with a reduced number of LMIs,” IEEE Trans. on Fuzzy Systems, Vol.23, No.4, pp. 1197-1210, 2015. https://doi.org/10.1109/TFUZZ.2014.2347995
- [35] H. Wang and G.-H. Yang, “Decentralized state feedback control of uncertain affine fuzzy large-scale systems with unknown interconnections,” IEEE Trans. on Fuzzy Systems, Vol.24, No.5, pp. 1134-1146, 2016. https://doi.org/10.1109/TFUZZ.2015.2504380
- [36] K. Tanaka and H. O. Wang, “Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach,” John Wiley & Sons, Inc., 2001. https://doi.org/10.1002/0471224596
- [37] L. Yu, “Robust control-linear matrix inequality processing,” Tsinghua University Press, 2002 (in Chinese).
This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.