American Institute of Mathematical Sciences

Advanced
doi: 10.3934/jimo.2020119

Fuzzy event-triggered disturbance rejection control of nonlinear systems

Peng Cheng 1, , Yanqing Liu 1, , Yanyan Yin 2, , Song Wang 3, and  Feng Pan 1,,

1. 

Key laboratory of Advanced Process Control for Light Industry (Ministry of Education), School of Internet of Things Engineering, Jiangnan University, Wuxi, 214122, China
2. 

School of Electrical Engineering, Computing and Mathematical Sciences, Curtin University, Perth, Western Australia, 6102, Australia
3. 

School of Electrical Engineering, Computing and Mathematical Sciences, Curtin University, GPO Box U1987, Perth, WA6845, Australia

* Corresponding author: Feng Pan

Received  October 2019 Revised  March 2020 Published  June 2020

The problem of fuzzy based event-triggered disturbance rejection control for nonlinear systems is addressed in this paper. A new fuzzy event based anti rejection controller is designed and a fuzzy reduced disturbance observer is constructed. Sufficient conditions for the closed loop system to be asymptotically stable under an $ H_\infty $ performance index are derived. Based on these conditions, the design of a fuzzy event-triggered state feedback controller is formulated and solved. Numerical results are presented to demonstrate the correctness and effectiveness of our theoretical findings.

Keywords: Fuzzy system, nonlinear systems, event trigger, disturbance rejection, asymptotically stable.
Mathematics Subject Classification: Primary: 93C55, 93D09; Secondary: 93B05.
Citation: Peng Cheng, Yanqing Liu, Yanyan Yin, Song Wang, Feng Pan. Fuzzy event-triggered disturbance rejection control of nonlinear systems. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020119
References:
[1]

A. Benzaouia and A. E. Hajjaji, Delay-dependent stabilization conditions of controlled positive T-S fuzzy systems with time varying delay, International Journal of Innovative Computing, Information and Control, 7 (2011), 1533-1548.   Google Scholar

[2]

Y.-Y. Cao, Z. L. Lin and Y. Shamash, Set invariance analysis and gain-scheduling control for LPV systems subject to actuator saturation, Systems and Control Letters, 46 (2002), 137-151.  doi: 10.1016/S0167-6911(02)00128-7.  Google Scholar

[3]

X. Chang and G. Yang, Relaxed results on stabilization and state feedback $H_\infty$ control conditions for T-S fuzzy systems, International Journal of Innovative Computing, Information and Control, 7 (2011), 1753-1764.   Google Scholar

[4]

M. Chen and W. Chen, Disturbance observer based robust control for time delay uncertain systems, International Journal of Control, Automation and Systems, 8 (2010), 445-453.   Google Scholar

[5]

T. M. Guerra and L. Vermeiren, LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno's form, Automatica J. IFAC, 40 (2004), 823-829.  doi: 10.1016/j.automatica.2003.12.014.  Google Scholar

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L. Guo and W.-H. Chen, Disturbance attenuation and rejection for systems with nonlinearity via DOBC approach, International Journal of Robust and Nonlinear Control, 15 (2005), 109-125.  doi: 10.1002/rnc.978.  Google Scholar

[7] L. Guo and S. Y. Cao, Anti-Disturbance Control for Systems with Multiple Disturbances, USA: CRC Press, Boca Raton, FL, 2014.  doi: 10.1201/b15528.  Google Scholar
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L. Guo and S. Y. Cao, Anti-disturbance control theory for systems with multiple disturbances: A survey, ISA Transactions, 53 (2014), 846-849.  doi: 10.1016/j.isatra.2013.10.005.  Google Scholar

[9]

T. Iwasaki, G. Meinsma and M. Y. Fu, Generalized S-procedure and finite frequency KYP lemma, Mathematical Problems in Engineering, 6 (2000), 305-320.  doi: 10.1155/S1024123X00001368.  Google Scholar

[10]

L. L. Lv, S. Y. Tang and L. Zhang, Parametric solutions to generalized periodic Sylvester bimatrix equations, Journal of the Franklin Institute, 357 (2020), 3601-3621.  doi: 10.1016/j.jfranklin.2019.12.031.  Google Scholar

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L. L. Lv and Z. Zhang, Finite iterative solutions to periodic Sylvester matrix equations, Journal of the Franklin Institute, 354 (2017), 2358-2370.  doi: 10.1016/j.jfranklin.2017.01.004.  Google Scholar

[12]

L. L. Lv, Z. Zhang, L. Zhang and X. X. Liu, Gradient based approach for generalized discrete-time periodic coupled Sylvester matrix equations, Journal of the Franklin Institute, 355 (2018), 7691-7705.  doi: 10.1016/j.jfranklin.2018.07.045.  Google Scholar

[13]

X. J. Su, P. Shi, L. Q. Wu and Y.-D. Song, A novel control design on discrete-time Takagi-Sugeno fuzzy systems with time-varying delays, IEEE Trans on Fuzzy Systems, 21 (2013), 655-671.  doi: 10.1109/TFUZZ.2012.2226941.  Google Scholar

[14]

C. Sun, Y. Wang and C. Chang, Switching T-S fuzzy model-based guaranteed cost control for two-wheeled mobile robots, International Journal of Innovative Computing, Information and Control, 8 (2012), 3015-3028.   Google Scholar

[15]

T. Takagi and M. Sugeno, Fuzzy identification of systems and its applications to modeling and control, IEEE Trans on Syst. Man Cybern, 15 (1985), 116-132.   Google Scholar

[16]

K. Tanaka, T. Hori and H. O. Wang, A multiple Lyapunov function approach to stabilization of fuzzy control systems, IEEE Trans on Fuzzy Syst., 11 (2003), 582-589.  doi: 10.1109/TFUZZ.2003.814861.  Google Scholar

[17]

L. Wu, X. Su, P. Shi and J. Qiu, Model approximation for discrete-time state-delay systems in the T-S fuzzy framework, IEEE Trans on Fuzzy Systems, 19 (2011), 366-378.   Google Scholar

[18]

X. M. Yao and L. Guo, Composite anti-disturbance control for Markovian jump nonlinear systems via disturbance observer, Automatica J. IFAC, 49 (2013), 2538-2545.  doi: 10.1016/j.automatica.2013.05.002.  Google Scholar

[19]

Y. Y. Yin, X. Chen and F. Liu, Disturbance rejection control for Markov jump systems with nonhomogeneous processes, The 27th Chinese Control and Decision Conference (2015 CCDC), Qingdao, China, (2015), 15340479. doi: 10.1109/CCDC.2015.7162007.  Google Scholar

[20]

Y. Y. Yin, Z. L. Lin, Y. Q. Liu and K. L. Teo, Event-triggered constrained control of positive systems with input saturation, International Journal of Robust and Nonlinear Control, 28 (2018), 3532-3542.  doi: 10.1002/rnc.4097.  Google Scholar

[21]

Y. Y. Yin, Y. Q. Liu, K. L. Teo and S. Wang, Event-triggered probabilistic robust control of linear systems with input constrains: By scenario optimization approach, International Journal of Robust and Nonlinear Control, 28 (2018), 144-153.  doi: 10.1002/rnc.3858.  Google Scholar

[22]

Y. Y. Yin, L. J. Zhu, F. Liu, K. L. Teo and S. Wang, Asynchronous $H_\infty$ control for nonhomogeneous higher-level Markov jump systems, Journal of the Franklin Institute, 357 (2020), 4697–4708. doi: 10.1016/j.jfranklin.2020.02.010.  Google Scholar

[23]

L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.  doi: 10.1016/S0019-9958(65)90241-X.  Google Scholar

[24]

H. B. Zeng, K. L. Teo, Y. He and W. Wang, Sampled-data-based dissipative control of T-S fuzzy systems, Applied Mathematical Modelling, 65 (2019), 415-427.  doi: 10.1016/j.apm.2018.08.012.  Google Scholar

[25]

H.-B. Zeng, K. L. Teo, Y. He and W. Wang, Sampled-data stabilization of chaotic systems based on a T-S fuzzy model, Information Sciences, 483 (2019), 262-272.  doi: 10.1016/j.ins.2019.01.046.  Google Scholar

show all references

References:
[1]

A. Benzaouia and A. E. Hajjaji, Delay-dependent stabilization conditions of controlled positive T-S fuzzy systems with time varying delay, International Journal of Innovative Computing, Information and Control, 7 (2011), 1533-1548.   Google Scholar

[2]

Y.-Y. Cao, Z. L. Lin and Y. Shamash, Set invariance analysis and gain-scheduling control for LPV systems subject to actuator saturation, Systems and Control Letters, 46 (2002), 137-151.  doi: 10.1016/S0167-6911(02)00128-7.  Google Scholar

[3]

X. Chang and G. Yang, Relaxed results on stabilization and state feedback $H_\infty$ control conditions for T-S fuzzy systems, International Journal of Innovative Computing, Information and Control, 7 (2011), 1753-1764.   Google Scholar

[4]

M. Chen and W. Chen, Disturbance observer based robust control for time delay uncertain systems, International Journal of Control, Automation and Systems, 8 (2010), 445-453.   Google Scholar

[5]

T. M. Guerra and L. Vermeiren, LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno's form, Automatica J. IFAC, 40 (2004), 823-829.  doi: 10.1016/j.automatica.2003.12.014.  Google Scholar

[6]

L. Guo and W.-H. Chen, Disturbance attenuation and rejection for systems with nonlinearity via DOBC approach, International Journal of Robust and Nonlinear Control, 15 (2005), 109-125.  doi: 10.1002/rnc.978.  Google Scholar

[7] L. Guo and S. Y. Cao, Anti-Disturbance Control for Systems with Multiple Disturbances, USA: CRC Press, Boca Raton, FL, 2014.  doi: 10.1201/b15528.  Google Scholar
[8]

L. Guo and S. Y. Cao, Anti-disturbance control theory for systems with multiple disturbances: A survey, ISA Transactions, 53 (2014), 846-849.  doi: 10.1016/j.isatra.2013.10.005.  Google Scholar

[9]

T. Iwasaki, G. Meinsma and M. Y. Fu, Generalized S-procedure and finite frequency KYP lemma, Mathematical Problems in Engineering, 6 (2000), 305-320.  doi: 10.1155/S1024123X00001368.  Google Scholar

[10]

L. L. Lv, S. Y. Tang and L. Zhang, Parametric solutions to generalized periodic Sylvester bimatrix equations, Journal of the Franklin Institute, 357 (2020), 3601-3621.  doi: 10.1016/j.jfranklin.2019.12.031.  Google Scholar

[11]

L. L. Lv and Z. Zhang, Finite iterative solutions to periodic Sylvester matrix equations, Journal of the Franklin Institute, 354 (2017), 2358-2370.  doi: 10.1016/j.jfranklin.2017.01.004.  Google Scholar

[12]

L. L. Lv, Z. Zhang, L. Zhang and X. X. Liu, Gradient based approach for generalized discrete-time periodic coupled Sylvester matrix equations, Journal of the Franklin Institute, 355 (2018), 7691-7705.  doi: 10.1016/j.jfranklin.2018.07.045.  Google Scholar

[13]

X. J. Su, P. Shi, L. Q. Wu and Y.-D. Song, A novel control design on discrete-time Takagi-Sugeno fuzzy systems with time-varying delays, IEEE Trans on Fuzzy Systems, 21 (2013), 655-671.  doi: 10.1109/TFUZZ.2012.2226941.  Google Scholar

[14]

C. Sun, Y. Wang and C. Chang, Switching T-S fuzzy model-based guaranteed cost control for two-wheeled mobile robots, International Journal of Innovative Computing, Information and Control, 8 (2012), 3015-3028.   Google Scholar

[15]

T. Takagi and M. Sugeno, Fuzzy identification of systems and its applications to modeling and control, IEEE Trans on Syst. Man Cybern, 15 (1985), 116-132.   Google Scholar

[16]

K. Tanaka, T. Hori and H. O. Wang, A multiple Lyapunov function approach to stabilization of fuzzy control systems, IEEE Trans on Fuzzy Syst., 11 (2003), 582-589.  doi: 10.1109/TFUZZ.2003.814861.  Google Scholar

[17]

L. Wu, X. Su, P. Shi and J. Qiu, Model approximation for discrete-time state-delay systems in the T-S fuzzy framework, IEEE Trans on Fuzzy Systems, 19 (2011), 366-378.   Google Scholar

[18]

X. M. Yao and L. Guo, Composite anti-disturbance control for Markovian jump nonlinear systems via disturbance observer, Automatica J. IFAC, 49 (2013), 2538-2545.  doi: 10.1016/j.automatica.2013.05.002.  Google Scholar

[19]

Y. Y. Yin, X. Chen and F. Liu, Disturbance rejection control for Markov jump systems with nonhomogeneous processes, The 27th Chinese Control and Decision Conference (2015 CCDC), Qingdao, China, (2015), 15340479. doi: 10.1109/CCDC.2015.7162007.  Google Scholar

[20]

Y. Y. Yin, Z. L. Lin, Y. Q. Liu and K. L. Teo, Event-triggered constrained control of positive systems with input saturation, International Journal of Robust and Nonlinear Control, 28 (2018), 3532-3542.  doi: 10.1002/rnc.4097.  Google Scholar

[21]

Y. Y. Yin, Y. Q. Liu, K. L. Teo and S. Wang, Event-triggered probabilistic robust control of linear systems with input constrains: By scenario optimization approach, International Journal of Robust and Nonlinear Control, 28 (2018), 144-153.  doi: 10.1002/rnc.3858.  Google Scholar

[22]

Y. Y. Yin, L. J. Zhu, F. Liu, K. L. Teo and S. Wang, Asynchronous $H_\infty$ control for nonhomogeneous higher-level Markov jump systems, Journal of the Franklin Institute, 357 (2020), 4697–4708. doi: 10.1016/j.jfranklin.2020.02.010.  Google Scholar

[23]

L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.  doi: 10.1016/S0019-9958(65)90241-X.  Google Scholar

[24]

H. B. Zeng, K. L. Teo, Y. He and W. Wang, Sampled-data-based dissipative control of T-S fuzzy systems, Applied Mathematical Modelling, 65 (2019), 415-427.  doi: 10.1016/j.apm.2018.08.012.  Google Scholar

[25]

H.-B. Zeng, K. L. Teo, Y. He and W. Wang, Sampled-data stabilization of chaotic systems based on a T-S fuzzy model, Information Sciences, 483 (2019), 262-272.  doi: 10.1016/j.ins.2019.01.046.  Google Scholar

Figure 1.  System trajectories under disturbance rejection controller
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Figure 2.  Estimation of disturbance
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