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Published in: Soft Computing 19/2020

01-04-2020 | Methodologies and Application

Fuzzy optimal control for nonlinear systems with time-varying delay via sampled-data controller

Authors: Zifang Qu, Zhengdi Zhang, Zhenbin Du, Tiebiao Zhao

Published in: Soft Computing | Issue 19/2020

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Abstract

This work is devoted to a fuzzy sampled-data optimal control problem for nonlinear systems with time-varying delay in Takagi–Sugeno fuzzy form. Based on the Lyapunov–Krasovskii functional theory, some novel stability criteria are established. A fuzzy sampled-data controller is developed to ensure that the fuzzy closed-loop sampled-data control system is asymptotically stable and the guaranteed cost performance is also minimized. It is shown that the obtained results are less conservative in the stability analysis. Two examples of the computer-simulated truck-trailer system and the continuous stirred tank reactor system are provided to show the effectiveness and the merits of the proposed design.

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Literature
go back to reference Cao Y-Y, Frank PM (2001) Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi–Sugeno fuzzy models. Fuzzy Sets Syst 124:213–229MathSciNetMATH Cao Y-Y, Frank PM (2001) Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi–Sugeno fuzzy models. Fuzzy Sets Syst 124:213–229MathSciNetMATH
go back to reference Chen B, Liu X-P (2015) Fuzzy guaranteed cost control for nonlinear systems with time-varying delay. IEEE Trans Fuzzy Syst 13(2):238–249 Chen B, Liu X-P (2015) Fuzzy guaranteed cost control for nonlinear systems with time-varying delay. IEEE Trans Fuzzy Syst 13(2):238–249
go back to reference Chen P, Han Q-L, Yue D, Tian E-G (2011) Sampled-data robust H∞ control for T–S fuzzy systems with time delay and uncertainties. Fuzzy Sets Syst 179:20–33MathSciNetMATH Chen P, Han Q-L, Yue D, Tian E-G (2011) Sampled-data robust H∞ control for T–S fuzzy systems with time delay and uncertainties. Fuzzy Sets Syst 179:20–33MathSciNetMATH
go back to reference Cloosterman M, van de Wouw N, Heemels W, Nijmeijer H (2009) Stability of networked control systems with uncertain time-varying delays. IEEE Trans Autom Control 54(7):1575–1580MathSciNetMATH Cloosterman M, van de Wouw N, Heemels W, Nijmeijer H (2009) Stability of networked control systems with uncertain time-varying delays. IEEE Trans Autom Control 54(7):1575–1580MathSciNetMATH
go back to reference Dong S-L, Su H-Y, Shi P, Lu R-Q, Wu Z-G (2017) Filtering for discrete-time switched fuzzy systems with quantization. IEEE Trans Fuzzy Syst 25(6):1616–1628 Dong S-L, Su H-Y, Shi P, Lu R-Q, Wu Z-G (2017) Filtering for discrete-time switched fuzzy systems with quantization. IEEE Trans Fuzzy Syst 25(6):1616–1628
go back to reference Du Z-B, Qin Z-K, Ren H-J, Lu Z-Y (2017) Fuzzy robust H∞ sampled-data control for uncertain nonlinear systems with time-varying delay. Int J Fuzzy Syst 19(5):1417–1429MathSciNet Du Z-B, Qin Z-K, Ren H-J, Lu Z-Y (2017) Fuzzy robust H sampled-data control for uncertain nonlinear systems with time-varying delay. Int J Fuzzy Syst 19(5):1417–1429MathSciNet
go back to reference Du Z-B, Yan Z-Z, Zhao Z (2019) Interval type-2 fuzzy tracking control for nonlinear systems via sampled-data controller. Fuzzy Sets Syst 356:92–112MathSciNetMATH Du Z-B, Yan Z-Z, Zhao Z (2019) Interval type-2 fuzzy tracking control for nonlinear systems via sampled-data controller. Fuzzy Sets Syst 356:92–112MathSciNetMATH
go back to reference Gao H-J, Chen T-W (2007) Stabilization of nonlinear systems under variable sampling: a fuzzy control approach. IEEE Trans Fuzzy Syst 15(5):972–983 Gao H-J, Chen T-W (2007) Stabilization of nonlinear systems under variable sampling: a fuzzy control approach. IEEE Trans Fuzzy Syst 15(5):972–983
go back to reference Ge X-H, Han Q-L, Jiang X-F (2014) Sampled-data H∞ filtering of Takagi–Sugeno fuzzy systems with interval time-varying delays. J Frankl Inst 351(5):2515–2542MathSciNetMATH Ge X-H, Han Q-L, Jiang X-F (2014) Sampled-data H∞ filtering of Takagi–Sugeno fuzzy systems with interval time-varying delays. J Frankl Inst 351(5):2515–2542MathSciNetMATH
go back to reference Huang J, Shi Y, Huang H-N, Li Z (2013) l2 − l∞ filtering for multirate nonlinear sampled-data systems using T–S fuzzy models. Digit Signal Proc 23(1):418–426 Huang J, Shi Y, Huang H-N, Li Z (2013) l2 − l∞ filtering for multirate nonlinear sampled-data systems using T–S fuzzy models. Digit Signal Proc 23(1):418–426
go back to reference Jiang X-F (2015) On sampled-data fuzzy control design approach for T–S model-based fuzzy systems by using discretization approach. Inf Sci 296:3071–3314MathSciNet Jiang X-F (2015) On sampled-data fuzzy control design approach for T–S model-based fuzzy systems by using discretization approach. Inf Sci 296:3071–3314MathSciNet
go back to reference Jiang B-P, Kao Y-G, Park JH, Gao C-C (2018) Stability and stabilization for singular switching semi-Markovian jump systems with generally uncertain transition rates. IEEE Trans Autom Control 63(11):3919–3926MathSciNetMATH Jiang B-P, Kao Y-G, Park JH, Gao C-C (2018) Stability and stabilization for singular switching semi-Markovian jump systems with generally uncertain transition rates. IEEE Trans Autom Control 63(11):3919–3926MathSciNetMATH
go back to reference Jing X-J, Lam HK, Shi P (2014) Fuzzy Sampled-data control for uncertain vehicle suspension systems. IEEE Trans Cybern 44(7):1111–1126 Jing X-J, Lam HK, Shi P (2014) Fuzzy Sampled-data control for uncertain vehicle suspension systems. IEEE Trans Cybern 44(7):1111–1126
go back to reference Katayama H, Ichikawa A (2004) H∞ control for sampled-data nonlinear systems described by Takagi–Sugeno fuzzy systems. Fuzzy Sets Syst 148:431–452MathSciNetMATH Katayama H, Ichikawa A (2004) H∞ control for sampled-data nonlinear systems described by Takagi–Sugeno fuzzy systems. Fuzzy Sets Syst 148:431–452MathSciNetMATH
go back to reference Kim DW, Lee HJ (2009) Stability connection between sampled-data fuzzy control systems with quantization and their approximate discrete-time model. Automatica 45(6):1518–1523MathSciNetMATH Kim DW, Lee HJ (2009) Stability connection between sampled-data fuzzy control systems with quantization and their approximate discrete-time model. Automatica 45(6):1518–1523MathSciNetMATH
go back to reference Kim DW, Lee HJ, Tomizuka M (2010) Fuzzy stabilization of nonlinear systems under sampled-data feedback: an exact discrete-time model approach. IEEE Trans Fuzzy Syst 18(2):251–260 Kim DW, Lee HJ, Tomizuka M (2010) Fuzzy stabilization of nonlinear systems under sampled-data feedback: an exact discrete-time model approach. IEEE Trans Fuzzy Syst 18(2):251–260
go back to reference Kim HJ, Koo GB, Park JB, Joo YH (2015) Decentralized sampled-data H∞ fuzzy filter for nonlinear large-scale systems. Fuzzy Sets Syst 273:68–86MathSciNetMATH Kim HJ, Koo GB, Park JB, Joo YH (2015) Decentralized sampled-data H fuzzy filter for nonlinear large-scale systems. Fuzzy Sets Syst 273:68–86MathSciNetMATH
go back to reference Kim HS, Park JB, Joo YH (2018) A fuzzy Lyapunov–Krasovskii functional approach to sampled-data output-feedback stabilization of polynomial fuzzy systems. IEEE Trans Fuzzy Syst 26(1):366–373 Kim HS, Park JB, Joo YH (2018) A fuzzy Lyapunov–Krasovskii functional approach to sampled-data output-feedback stabilization of polynomial fuzzy systems. IEEE Trans Fuzzy Syst 26(1):366–373
go back to reference Koo GB, Park JB, Joo YH (2012) Exponential mean-square stabilisation for non-linear systems: sampled-data fuzzy control approach. IET Control Theory Appl 6(18):2765–2774MathSciNet Koo GB, Park JB, Joo YH (2012) Exponential mean-square stabilisation for non-linear systems: sampled-data fuzzy control approach. IET Control Theory Appl 6(18):2765–2774MathSciNet
go back to reference Koo GB, Park JB, Joo YH (2013) Guaranteed cost sampled-data fuzzy control for non-linear systems: a continuous-time Lyapunov approach. IET Control Theory Appl 13:1745–1752MathSciNet Koo GB, Park JB, Joo YH (2013) Guaranteed cost sampled-data fuzzy control for non-linear systems: a continuous-time Lyapunov approach. IET Control Theory Appl 13:1745–1752MathSciNet
go back to reference Koo GB, Park JB, Joo YH (2016) Intelligent digital redesign for non-linear systems:observer-based sampled-data fuzzy control approach. IET Control Theory Appl 10(1):1–9MathSciNet Koo GB, Park JB, Joo YH (2016) Intelligent digital redesign for non-linear systems:observer-based sampled-data fuzzy control approach. IET Control Theory Appl 10(1):1–9MathSciNet
go back to reference Lam HK (2012) Stabilization of nonlinear systems using sampled-data output-feedback fuzzy controller based on polynomial-fuzzy-model-based control approach. IEEE Trans Syst Man Cybern B 42(1):258–267 Lam HK (2012) Stabilization of nonlinear systems using sampled-data output-feedback fuzzy controller based on polynomial-fuzzy-model-based control approach. IEEE Trans Syst Man Cybern B 42(1):258–267
go back to reference Lam HK, Leung FH (2007) Sampled-data fuzzy controller for time delay nonlinear systems: fuzzy-model-based LMI approach. IEEE Trans Syst Man Cybern B 37(3):617–629 Lam HK, Leung FH (2007) Sampled-data fuzzy controller for time delay nonlinear systems: fuzzy-model-based LMI approach. IEEE Trans Syst Man Cybern B 37(3):617–629
go back to reference Lam HK, Ling WK (2008) Sampled-data fuzzy controller for continuous nonlinear systems. IET Control Theory Appl 2(1):32–39MathSciNet Lam HK, Ling WK (2008) Sampled-data fuzzy controller for continuous nonlinear systems. IET Control Theory Appl 2(1):32–39MathSciNet
go back to reference Lam HK, Seneviratne LD (2009) Tracking control of sampled-data fuzzy-model-based control systems. IET Control Theory Appl 3(1):56–67MathSciNet Lam HK, Seneviratne LD (2009) Tracking control of sampled-data fuzzy-model-based control systems. IET Control Theory Appl 3(1):56–67MathSciNet
go back to reference Lee TH, Park JH (2018) New methods of fuzzy sampled-data control for stabilization of chaotic systems. IEEE Trans Syst Man Cybern B 48(12):2026–2034 Lee TH, Park JH (2018) New methods of fuzzy sampled-data control for stabilization of chaotic systems. IEEE Trans Syst Man Cybern B 48(12):2026–2034
go back to reference Li H-Y, Sun X-J, Shi P, Lam HK (2015) Control design of interval type-2 fuzzy systems with actuator fault: sampled-data control approach. Inf Sci 302:1–13MATH Li H-Y, Sun X-J, Shi P, Lam HK (2015) Control design of interval type-2 fuzzy systems with actuator fault: sampled-data control approach. Inf Sci 302:1–13MATH
go back to reference Lien C-H, Yu K-W, Huang C-T, Chou P-Y, Chung L-Y, Chen J-D (2010) Robust H∞ control for uncertain T–S fuzzy time-delay systems with sampled-data input and nonlinear perturbations. Nonlinear Anal: Hybrid Syst 4(3):550–556MathSciNetMATH Lien C-H, Yu K-W, Huang C-T, Chou P-Y, Chung L-Y, Chen J-D (2010) Robust H control for uncertain T–S fuzzy time-delay systems with sampled-data input and nonlinear perturbations. Nonlinear Anal: Hybrid Syst 4(3):550–556MathSciNetMATH
go back to reference Liu Y-J, Lee S-M (2016) Stability and stabilization of Takagi–Sugeno fuzzy systems via sampled-data and state quantized controller. IEEE Trans Fuzzy Syst 24(3):635–644 Liu Y-J, Lee S-M (2016) Stability and stabilization of Takagi–Sugeno fuzzy systems via sampled-data and state quantized controller. IEEE Trans Fuzzy Syst 24(3):635–644
go back to reference Liu H, Zhou G-P (2015) Finite-time sampled-data control for switching T–S fuzzy systems. Neurocomputing 166(20):294–300 Liu H, Zhou G-P (2015) Finite-time sampled-data control for switching T–S fuzzy systems. Neurocomputing 166(20):294–300
go back to reference Liu Y-J, Park JH, Guo B-Z, Shu Y-J (2018) Further results on stabilization of chaotic systems based on fuzzy memory sampled-data control. IEEE Trans Syst Man Cybern B 26(2):1040–1045 Liu Y-J, Park JH, Guo B-Z, Shu Y-J (2018) Further results on stabilization of chaotic systems based on fuzzy memory sampled-data control. IEEE Trans Syst Man Cybern B 26(2):1040–1045
go back to reference Nishikawa M, Katayama H, Yoneyama J, Ichikawa A (2000) Design of output feedback controllers for sampled-data fuzzy systems. Int J Syst Sci 31(9):438–449MATH Nishikawa M, Katayama H, Yoneyama J, Ichikawa A (2000) Design of output feedback controllers for sampled-data fuzzy systems. Int J Syst Sci 31(9):438–449MATH
go back to reference Syed Ali M, Gunasekaran N, Zhu Q-X (2017) State estimation of T–S fuzzy delayed neural networks with Markovian jumping parameters using sampled-data control. Fuzzy Sets Syst 306:87–104MathSciNetMATH Syed Ali M, Gunasekaran N, Zhu Q-X (2017) State estimation of T–S fuzzy delayed neural networks with Markovian jumping parameters using sampled-data control. Fuzzy Sets Syst 306:87–104MathSciNetMATH
go back to reference Takagi T, Sugeno M (1985) Fuzzy identification of systems and its applications to modeling and control. IEEE Trans Syst Man Cybern SMC 15(1):116–132MATH Takagi T, Sugeno M (1985) Fuzzy identification of systems and its applications to modeling and control. IEEE Trans Syst Man Cybern SMC 15(1):116–132MATH
go back to reference Tang P-Y, Ma Y-C (2019) Exponential stabilization and sampled-data H∞ control for uncertain T–S fuzzy systems with time-varying delay. J Frankl Inst 356:4859–4887MATH Tang P-Y, Ma Y-C (2019) Exponential stabilization and sampled-data H control for uncertain T–S fuzzy systems with time-varying delay. J Frankl Inst 356:4859–4887MATH
go back to reference Wag M, Qiu J-B, Chadli M, Wang M (2016) A switched system approach to exponential stabilization of sampled-data T–S fuzzy systems with packet dropouts. IEEE Trans Cybern 46(12):3145–3156 Wag M, Qiu J-B, Chadli M, Wang M (2016) A switched system approach to exponential stabilization of sampled-data T–S fuzzy systems with packet dropouts. IEEE Trans Cybern 46(12):3145–3156
go back to reference Wang J-W, Li H-X, Wu H-N (2016) Fuzzy guaranteed cost sampled-data control of nonlinear systems coupled with a scalar reaction-diffusion process. Fuzzy Sets Syst 302:121–142MathSciNetMATH Wang J-W, Li H-X, Wu H-N (2016) Fuzzy guaranteed cost sampled-data control of nonlinear systems coupled with a scalar reaction-diffusion process. Fuzzy Sets Syst 302:121–142MathSciNetMATH
go back to reference Wang B, Cheng J, Al-Barakati A, Fardoun HM (2017) A mismatched membership function approach to sampled-data stabilization for T–S fuzzy systems with time-varying delayed signals. Signal Proc 140:161–170 Wang B, Cheng J, Al-Barakati A, Fardoun HM (2017) A mismatched membership function approach to sampled-data stabilization for T–S fuzzy systems with time-varying delayed signals. Signal Proc 140:161–170
go back to reference Wang YY, Karimi HR, Lam HK, Shen H (2018) An improved result on exponential stabilization of sampled-data fuzzy systems. IEEE Trans Fuzzy Syst 26(6):3875–3883 Wang YY, Karimi HR, Lam HK, Shen H (2018) An improved result on exponential stabilization of sampled-data fuzzy systems. IEEE Trans Fuzzy Syst 26(6):3875–3883
go back to reference Wang Y-Y, Xia Y-Q, Ahn CK, Zhu Y-Z (2019a) Exponential stabilization of Takagi–Sugeno fuzzy systems with aperiodic sampling: an aperiodic adaptive Event-Triggered method. IEEE Trans Syst Man Cybern B 49(2):444–454 Wang Y-Y, Xia Y-Q, Ahn CK, Zhu Y-Z (2019a) Exponential stabilization of Takagi–Sugeno fuzzy systems with aperiodic sampling: an aperiodic adaptive Event-Triggered method. IEEE Trans Syst Man Cybern B 49(2):444–454
go back to reference Wu Z-G, Shi P, Su H-Y, Chu J (2014) Sampled-data fuzzy control of chaotic systems based on a T–S fuzzy model. IEEE Trans Fuzzy Syst 22(1):153–163 Wu Z-G, Shi P, Su H-Y, Chu J (2014) Sampled-data fuzzy control of chaotic systems based on a T–S fuzzy model. IEEE Trans Fuzzy Syst 22(1):153–163
go back to reference Wu Z-G, Dong S-L, Shi P, Su H-Y, Huang T-W, Lu R-Q (2017) Fuzzy-model-based nonfragile guaranteed cost control of nonlinear Markov jump systems. IEEE Trans Syst Man Cybern 47(8):2388–2397 Wu Z-G, Dong S-L, Shi P, Su H-Y, Huang T-W, Lu R-Q (2017) Fuzzy-model-based nonfragile guaranteed cost control of nonlinear Markov jump systems. IEEE Trans Syst Man Cybern 47(8):2388–2397
go back to reference Wu Z-G, Dong S-L, Su H-Y, Li C-D (2018) Asynchronous dissipative control for fuzzy Markov jump systems. IEEE Trans Cybern 48(8):2426–2436 Wu Z-G, Dong S-L, Su H-Y, Li C-D (2018) Asynchronous dissipative control for fuzzy Markov jump systems. IEEE Trans Cybern 48(8):2426–2436
go back to reference Yang D-Y, Cai K-Y (2008) Reliable H∞ non-uniform sampling fuzzy control for nonlinear systems with time delay. IEEE Trans Syst Man Cybern B 38(6):1606–1613 Yang D-Y, Cai K-Y (2008) Reliable H non-uniform sampling fuzzy control for nonlinear systems with time delay. IEEE Trans Syst Man Cybern B 38(6):1606–1613
go back to reference Yang F-S, Zhang H-G, Wang Y-C (2014) An enhanced input-delay approach to sampled-data stabilization of T–S fuzzy systems via mixed convex combination. Nonlinear Dyn 75(3):501–512MathSciNetMATH Yang F-S, Zhang H-G, Wang Y-C (2014) An enhanced input-delay approach to sampled-data stabilization of T–S fuzzy systems via mixed convex combination. Nonlinear Dyn 75(3):501–512MathSciNetMATH
go back to reference Yoneyama J (2011) Robust guaranteed cost control of uncertain fuzzy systems under time-varying sampling. Appl Soft Comput 11(1):249–255 Yoneyama J (2011) Robust guaranteed cost control of uncertain fuzzy systems under time-varying sampling. Appl Soft Comput 11(1):249–255
go back to reference Yoneyama J (2012) Robust sampled-data stabilization of uncertain fuzzy systems via input delay approach. Inf Sci 198:169–176MathSciNetMATH Yoneyama J (2012) Robust sampled-data stabilization of uncertain fuzzy systems via input delay approach. Inf Sci 198:169–176MathSciNetMATH
go back to reference Zeng H-B, Teo KL, He Y, Wang W (2019) Sampled-data-based dissipative control of T–S fuzzy systems. Appl Math Model 65:415–427MathSciNetMATH Zeng H-B, Teo KL, He Y, Wang W (2019) Sampled-data-based dissipative control of T–S fuzzy systems. Appl Math Model 65:415–427MathSciNetMATH
go back to reference Zhu X-L, Chen B, Yue D, Wang Y-Y (2012) An improved input delay approach to stabilization of fuzzy systems under variable sampling. IEEE Trans Fuzzy Syst 20(2):330–341 Zhu X-L, Chen B, Yue D, Wang Y-Y (2012) An improved input delay approach to stabilization of fuzzy systems under variable sampling. IEEE Trans Fuzzy Syst 20(2):330–341
go back to reference Zhu X-L, Chen B, Wang Y-Y, Yue D (2013) H∞ stabilization criterion with less complexity for nonuniform sampling fuzzy systems. Fuzzy Sets Syst 225:58–73MathSciNetMATH Zhu X-L, Chen B, Wang Y-Y, Yue D (2013) H stabilization criterion with less complexity for nonuniform sampling fuzzy systems. Fuzzy Sets Syst 225:58–73MathSciNetMATH
Metadata
Title
Fuzzy optimal control for nonlinear systems with time-varying delay via sampled-data controller
Authors
Zifang Qu
Zhengdi Zhang
Zhenbin Du
Tiebiao Zhao
Publication date
01-04-2020
Publisher
Springer Berlin Heidelberg
Published in
Soft Computing / Issue 19/2020
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-020-04827-6

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