Intelligent Digital Redesign for Nonlinear Interconnected Systems using Decentralized Fuzzy Control

Title & Authors
Intelligent Digital Redesign for Nonlinear Interconnected Systems using Decentralized Fuzzy Control
Koo, Geun-Bum; Park, Jin-Bae; Joo, Young-Hoon;

Abstract
In this paper, a novel intelligent digital redesign (IDR) technique is proposed for the nonlinear interconnected systems which can be represented by a Takagi-Sugeno (T-S) fuzzy model. The IDR technique is to convert a pre-designed analog controller into an equivalent digital one. To develop this method, the discretized models of the analog and digital closed-loop system with the decentralized controller are presented, respectively. Using these discretized models, the digital decentralized control gain is obtained to minimize the norm between the state variables of the analog and digital closed-loop systems and stabilize the digital closed-loop system. Its sufficient conditions are derived in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to verify the effectiveness of the proposed technique.
Keywords
Nonlinear interconnected systems;Takagi-Sugeno (T-S) fuzzy model;Decentralized control;Intelligent digital redesign (IDR);Linear matrix inequality (LMI);
Language
English
Cited by
1.
Decentralised control for large-scale sampled-data systems: digital redesign approach, International Journal of Control, 2015, 88, 11, 2181
2.
On the Fuzzy Model Predictive Control of Interconnected Nonlinear Systems, Arabian Journal for Science and Engineering, 2017, 42, 7, 2759
3.
Sampled-Data Observer-Based Decentralized Fuzzy Control for Nonlinear Large-Scale Systems, Journal of Electrical Engineering and Technology, 2016, 11, 3, 724
References
1.
X. G. Yan, J. J. Wang, X. Y. Lű, and S. Y. Zhang, "Decentralized output feedback robust stabilization for a class of nonlinear interconnected systems with similarity," IEEE Trans. Automatic Control, vol. 43, no. 2, pp. 294-299, 1998.

2.
X. G. Yan, C. Edwards, and S. K. Spurgeon, "Decentralised robust sliding mode control for a class of nonlinear interconnected systems by static output feedback," Automatica, vol. 40, pp. 613-620, 2004.

3.
B. Y. Zhu, Q. L. Zhang, and X. F. Zhang, "Decentralized robust guaranteed cost control for uncertain T-S fuzzy interconnected systems with time delays," Int. J. Information and Systems Sciences, vol. 1, no. 1, pp. 73-88, 2005.

4.
C. S. Tseng and B. S. Chen, "$H_{\infty}$ decentralized fuzzy model reference tracking control design for nonlinear interconnected systems," IEEE Trans. Fuzzy Systems, vol. 9, no. 6, pp. 795-809, 2001.

5.
F. H. Hsiao, C. W. Chen, Y. W. Liang, S. D. Xu, and W. L. Chiang, "T-S fuzzy controllers for nonlinear interconnected systems with multiple time delays," IEEE Trans. Circuits and Systems, vol. 52, no. 9, pp. 1883-1893, 2005.

6.
R. J. Wang, "Nonlinear decentralized state feedback controller for uncertain fuzzy time-delay interconnected systems," Fuzzy Sets and Systems, vol. 151, pp. 194-204, 2005.

7.
B. Song, "Robust stabilization of decentralized dynamic surface control for a class of interconnected nonlinear systems," Int. J. Control, Automation, and Systems, vol. 5, no. 2, pp. 138-146, 2007.

8.
S. Ganapathy and S. Velusami, "Decentralized loadfrequency control of interconnected power systems with SMES units and governor dead band using multi-objective evolutionary algorithm," J. Electrical Engineering and Technology, vol. 4, no. 4, pp. 443-450, 2009.

9.
D. K. Sambariya and R.Gupta, "Fuzzy applications in a multi-machine power system stabilizer," J. Electrical Engineering and Technology, vol. 5, no. 3, pp. 503-510, 2010.

10.
B. C. Kuo, Digital Control System: Holt, Rinehart and Winston, New York, 1980.

11.
L. S. Shieh, W. M. Wang, and J. S. H. Tsai, "Digital modeling and digital redesign of sampled-data uncertain systems," IEE Control Theory, vol. 142, pp. 585-594, 1995.

12.
L. S. Shieh, W. M. Wang, and J. B. Zheng, "Robust control of sampled-data uncertain systems using digitally redesigned observer-based controllers," Int. J. Control, vol. 66, pp. 43-64, 1997.

13.
Y. H. Joo, G. Chen, and L. S. Shieh, "Hybrid statespace fuzzy model-based controller with dual-rate sampling for digital control of chaotic systems," IEEE Trans. Fuzzy Systems, vol. 7, no. 4 pp. 394-408, 1999.

14.
W. Chang, J. B. Park, Y. H. Joo, and G. Chen, "Design of sampled-data fuzzy-model-based control systems by using intelligent digital redesign," IEEE Trans. Circuits and Systems, vol. 49, no. 4, pp. 509- 517, 2002.

15.
H. J. Lee, H. B. Kim, Y. H. Joo, W. Chang, and J. B. Park, "A new intelligent digital redesign for T-S fuzzy systems: global approach," IEEE Trans. Fuzzy Systems, vol. 12, no. 2, pp. 274-284, 2004.

16.
D. W. Kim, J. B. Park, and Y. H. Joo, "Effective digital implementation of fuzzy control systems based on approximate discrete-time models," Automatica, vol. 43, no. 10, pp. 1671-1683, 2007.

17.
H. C. Sung, D. W. Kim, J. B. Park, and Y. H. Joo, "Robust digital control of fuzzy systems with parametric uncertainties: LMI-based digital redesign approach," Fuzzy Sets and Systems, vol. 161, pp. 919-933, 2010.

18.
K. H. Lee, "Robust decentralized stabilization of a class of linear discrete-time systems with non-linear interactions," Int. J. Control, vol. 80, no. 10, pp. 1544-1551, 2007.

19.
Z. Duan, J. Wang, and L. Huang, "Special decentralized control problems in discrete-time interconnected systems composed of two subsystems," Systems and Control Letters, vol. 56, pp. 206-214, 2007.

20.
J. S. Tsai, N. Hu, P. Yang, S. Guo, and L. Shieh, "Modeling of decentralized linear observer and tracker for a class of unknown interconnected largescale sampled-data nonlinear systems with closedloop decoupling property," Computers and Mathematics with Applications, vol. 60, pp. 541-562, 2010.

21.
J. V. D. Oliveira, J. Bernussou, and J. C. Geromel, "A new discrete-time robust stability condition," Systems and Control Letters, vol. 37, pp. 261-265, 1999.

22.
F. Da, "Decentralized sliding mode adaptive controller design based on fuzzy neural networks for inter-connected uncertain nonlinear systems," IEEE Trans. Neural Networks, vol. 11, no. 6, pp. 1471-1480, 2000.