American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Two-period pricing and ordering decisions of perishable products with a learning period for demand disruption
  • JIMO Home
  • This Issue
  • Next Article
    Pricing vulnerable options under a jump-diffusion model with fast mean-reverting stochastic volatility
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

[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

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
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 2.  Estimation of disturbance
Figure Options

Download full-size image

Download as PowerPoint slide

[1]

Sishu Shankar Muni, Robert I. McLachlan, David J. W. Simpson. Homoclinic tangencies with infinitely many asymptotically stable single-round periodic solutions. Discrete & Continuous Dynamical Systems, 2021, 41 (8) : 3629-3650. doi: 10.3934/dcds.2021010
[2]

Masashi Wakaiki, Hideki Sano. Stability analysis of infinite-dimensional event-triggered and self-triggered control systems with Lipschitz perturbations. Mathematical Control & Related Fields, 2021  doi: 10.3934/mcrf.2021021
[3]

Emma D'Aniello, Saber Elaydi. The structure of $ \omega $-limit sets of asymptotically non-autonomous discrete dynamical systems. Discrete & Continuous Dynamical Systems - B, 2020, 25 (3) : 903-915. doi: 10.3934/dcdsb.2019195
[4]

Guanwei Chen, Martin Schechter. Multiple solutions for Schrödinger lattice systems with asymptotically linear terms and perturbed terms. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021124
[5]

Javad Taheri, Abolfazl Mirzazadeh. Optimization of inventory system with defects, rework failure and two types of errors under crisp and fuzzy approach. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021068
[6]

İsmail Özcan, Sirma Zeynep Alparslan Gök. On cooperative fuzzy bubbly games. Journal of Dynamics & Games, 2021  doi: 10.3934/jdg.2021010
[7]

Yanqin Fang, Jihui Zhang. Multiplicity of solutions for the nonlinear Schrödinger-Maxwell system. Communications on Pure & Applied Analysis, 2011, 10 (4) : 1267-1279. doi: 10.3934/cpaa.2011.10.1267
[8]

Manoel J. Dos Santos, Baowei Feng, Dilberto S. Almeida Júnior, Mauro L. Santos. Global and exponential attractors for a nonlinear porous elastic system with delay term. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2805-2828. doi: 10.3934/dcdsb.2020206
[9]

Yinsong Bai, Lin He, Huijiang Zhao. Nonlinear stability of rarefaction waves for a hyperbolic system with Cattaneo's law. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021049
[10]

Pengfei Wang, Mengyi Zhang, Huan Su. Input-to-state stability of infinite-dimensional stochastic nonlinear systems. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021066
[11]

Jianfeng Lv, Yan Gao, Na Zhao. The viability of switched nonlinear systems with piecewise smooth Lyapunov functions. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1825-1843. doi: 10.3934/jimo.2020048
[12]

Hong Yi, Chunlai Mu, Guangyu Xu, Pan Dai. A blow-up result for the chemotaxis system with nonlinear signal production and logistic source. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2537-2559. doi: 10.3934/dcdsb.2020194
[13]

Kuan-Hsiang Wang. An eigenvalue problem for nonlinear Schrödinger-Poisson system with steep potential well. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021030
[14]

Kazuhiro Kurata, Yuki Osada. Variational problems associated with a system of nonlinear Schrödinger equations with three wave interaction. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021100
[15]

Xu Pan, Liangchen Wang. Boundedness and asymptotic stability in a quasilinear two-species chemotaxis system with nonlinear signal production. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021064
[16]

Maoding Zhen, Binlin Zhang, Vicenţiu D. Rădulescu. Normalized solutions for nonlinear coupled fractional systems: Low and high perturbations in the attractive case. Discrete & Continuous Dynamical Systems, 2021, 41 (6) : 2653-2676. doi: 10.3934/dcds.2020379
[17]

Cheng-Kai Hu, Fung-Bao Liu, Hong-Ming Chen, Cheng-Feng Hu. Network data envelopment analysis with fuzzy non-discretionary factors. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1795-1807. doi: 10.3934/jimo.2020046
[18]

Haripriya Barman, Magfura Pervin, Sankar Kumar Roy, Gerhard-Wilhelm Weber. Back-ordered inventory model with inflation in a cloudy-fuzzy environment. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1913-1941. doi: 10.3934/jimo.2020052
[19]

Yosra Soussi. Stable recovery of a non-compactly supported coefficient of a Schrödinger equation on an infinite waveguide. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2021022
[20]

Yohei Yamazaki. Center stable manifolds around line solitary waves of the Zakharov–Kuznetsov equation with critical speed. Discrete & Continuous Dynamical Systems, 2021, 41 (8) : 3579-3614. doi: 10.3934/dcds.2021008

2019 Impact Factor: 1.366

Tools

Article outline

Figures and Tables

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences