Non-fragile control design for interval-valued fuzzy systems against nonlinear actuator faults. (English) Zbl 1423.93195
Summary: In this paper, we consider the reliable non-fragile \(H_\infty\) control design problem for a class of discrete-time interval-valued fuzzy systems with actuator faults. More precisely, the actuator fault model considered in the controller design consists of linear and nonlinear fault terms. The main focus of this paper is to design a non-fragile state feedback controller that is characterized by membership functions described by upper and lower membership functions and nonlinear weighting functions. It should be mentioned that the proposed interval-valued fuzzy system and the controller do not share same membership functions. A novel set of sufficient conditions is obtained by transforming the controller design problem into a multi-objective convex optimization problem based on the linear matrix inequality and the Lyapunov functional approaches, which ensures the robust asymptotic stability of the addressed system with a desired \(H_\infty\) performance index. Finally, two numerical examples, including an application-oriented model, mass-spring-damping system are presented to demonstrate the effectiveness of the proposed design technique.
MSC:
| 93C42 | Fuzzy control/observation systems |
| 93B36 | \(H^\infty\)-control |
| 93B52 | Feedback control |
| 93C73 | Perturbations in control/observation systems |
References:
| [1] | Bai, L.; Zhou, Q.; Wang, L.; Yu, Z.; Li, H., Observer-based adaptive control for stochastic nonstrict-feedback systems with unknown backlash-like hysteresis, Int. J. Adapt. Control Signal Process., 31, 1481-1490 (2017) · Zbl 1376.93058 |
| [2] | Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V., Linear Matrix Inequalities in System and Control Theory (1994), SIAM: SIAM Philadelphia · Zbl 0816.93004 |
| [3] | Chadli, M.; Karimi, H. R.; Shi, P., On stability and stabilization of singular uncertain Takagi-Sugeno fuzzy systems, J. Franklin Inst., 351, 1453-1463 (2014) · Zbl 1395.93459 |
| [4] | Feng, Z.; Zheng, W. X., Improved stability condition for Takagi-Sugeno fuzzy systems with time-varying delay, IEEE Trans. Cybern., 47, 661-670 (2017) |
| [5] | Gao, Y.; Li, H.; Chadli, M.; Lam, H. K., Static output-feedback control for interval type-2 discrete-time fuzzy systems, Complexity, 21, 74-88 (2016) |
| [6] | Hassani, H.; Zarei, J.; Chadli, M.; Qiu, J., Unknown input observer design for interval type-2 T-S fuzzy systems with immeasurable premise variables, IEEE Trans. Cybern., 47, 2639-2650 (2016) |
| [7] | Jin, Y.; Fu, J.; Zhang, Y.; Jing, Y., Reliable control of a class of switched cascade nonlinear systems with its application to flight control, Nonlinear Anal. Hybrid Syst., 11, 11-21 (2014) · Zbl 1291.93246 |
| [8] | Kwon, O. M.; Park, M. J.; Lee, S. M.; Park, Ju H., Augmented Lyapunov-Krasovskii functional approaches to robust stability criteria for uncertain Takagi-Sugeno fuzzy systems with time-varying delays, Fuzzy Sets Syst., 201, 1-19 (2012) · Zbl 1251.93072 |
| [9] | Lam, H. K.; Leung, F., Sampled-data fuzzy controller for time-delay nonlinear systems: fuzzy-model-based LMI approach, IEEE Trans. Syst. Man Cybern., Part B, Cybern., 37, 617-629 (2007) |
| [10] | Lam, H. K.; Li, H.; Deters, C.; Wuerdemann, H.; Secco, E.; Althoefer, K., Control design for interval type-2 fuzzy systems under imperfect premise matching, IEEE Trans. Ind. Electron., 61, 956-968 (2014) |
| [11] | Lam, H. K.; Seneviratne, L. D., Stability analysis of interval type-2 fuzzy-model-based control systems, IEEE Trans. Syst. Man Cybern., Part B, Cybern., 38, 617-628 (2008) |
| [12] | Li, H.; Liu, H.; Gao, H.; Shi, P., Reliable fuzzy control for active suspension systems with actuator delay and fault, IEEE Trans. Fuzzy Syst., 22, 342-357 (2012) |
| [13] | Li, H.; Pan, Y.; Zhou, Q., Filter design for interval type-2 fuzzy systems with \(D\) stability constraints under a unified frame, IEEE Trans. Fuzzy Syst., 23, 719-725 (2015) |
| [14] | Li, H.; Wang, J.; Wu, L.; Lam, H. K.; Gao, Y., Optimal guaranteed cost sliding mode control of interval type-2 fuzzy time-delay systems, IEEE Trans. Fuzzy Syst., 26, 246-257 (2018) |
| [15] | Li, H.; Wu, C.; Shi, P.; Gao, Y., Control of nonlinear networked systems with packet dropouts: interval type-2 fuzzy model-based approach, IEEE Trans. Cybern., 45, 2378-2389 (2015) |
| [16] | Li, H.; Yu, J.; Hilton, C.; Liu, H., Adaptive sliding mode control for nonlinear active suspension vehicle systems using T-S fuzzy approach, IEEE Trans. Ind. Electron., 60, 3328-3338 (2013) |
| [17] | Liu, C.; Sun, Z.; Shi, K.; Wang, F., Robust dynamic output feedback control for attitude stabilization of spacecraft with nonlinear perturbations, Aerosp. Sci. Technol., 64, 102-121 (2017) |
| [18] | Liu, W.; Lim, C. C.; Shi, P.; Xu, S., Sampled-data fuzzy control for a class of nonlinear systems with missing data and disturbances, Fuzzy Sets Syst., 306, 63-86 (2017) · Zbl 1368.93325 |
| [19] | Liu, Y.; Guo, B. Z.; Park, Ju H., Non-fragile \(H_\infty\) filtering for delayed Takagi-Sugeno fuzzy systems with randomly occurring gain variations, Fuzzy Sets Syst., 316, 99-116 (2017) · Zbl 1392.93048 |
| [20] | Mendel, J. M.; Karnik, N. N.; Liang, Q., Type-2 fuzzy logic systems, IEEE Trans. Fuzzy Syst., 7, 643-658 (1999) |
| [21] | Park, M. J.; Kwon, O. M., Stability and stabilization of discrete-time T-S fuzzy systems with time-varying delay via Cauchy-Schwartz-based summation inequality, IEEE Trans. Fuzzy Syst., 25, 128-140 (2017) |
| [22] | Sakthivel, R.; Saravanakumar, T.; Kaviarasan, B.; Lim, Y., Finite-time dissipative based fault-tolerant control of Takagi-Sugeno fuzzy systems in a network environment, J. Franklin Inst., 354, 3430-3454 (2017) · Zbl 1364.93423 |
| [23] | Sakthivel, R.; Wang, C.; Santra, S.; Kaviarasan, B., Non-fragile reliable sampled-data controller for nonlinear switched time-varying systems, Nonlinear Anal. Hybrid Syst., 27, 62-76 (2018) · Zbl 1378.93078 |
| [24] | Takagi, T.; Sugeno, M., Fuzzy identification of systems and its applications to modeling and control, IEEE Trans. Syst. Man Cybern., 15, 116-132 (1985) · Zbl 0576.93021 |
| [25] | Wu, L.; Yang, X.; Li, F., Non-fragile output tracking control of hypersonic air-breathing vehicles with an LPV model, IEEE/ASME Trans. Mechatron., 18, 1280-1288 (2013) |
| [26] | Wu, Y. Q.; Su, H.; Lu, R.; Wu, Z. G.; Shu, Z., Passivity-based non-fragile control for Markovian jump systems with aperiodic sampling, Syst. Control Lett., 84, 35-43 (2015) · Zbl 1326.93082 |
| [27] | Yang, J.; Zhong, S.; Xiong, L., A descriptor system approach to non-fragile \(H_\infty\) control for uncertain fuzzy neutral systems, Fuzzy Sets Syst., 160, 423-438 (2009) · Zbl 1175.93136 |
| [28] | Zhang, S.; Wang, Z.; Ding, D.; Dong, H.; Alsaadi, F. E.; Hayat, T., Non-fragile \(H_\infty\) fuzzy filtering with randomly occurring gain variations and channel fadings, IEEE Trans. Fuzzy Syst., 24, 505-518 (2016) |
| [29] | Zhao, X.; Zhang, L.; Shi, P.; Karimi, H. R., Novel stability criteria for T-S fuzzy systems, IEEE Trans. Fuzzy Syst., 22, 313-323 (2014) |
| [30] | Zhou, J.; Park, Ju H.; Ma, Q., Non-fragile observer-based \(H_\infty\) control for stochastic time-delay systems, Appl. Math. Comput., 291, 69-83 (2016) · Zbl 1410.93117 |
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