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Published in: Neural Computing and Applications 9/2018

31-08-2016 | Original Article

A new global fuzzy fault-tolerant control for a double inverted pendulum based on time-delay replacement

Authors: Tao Guo, Jing Xiong

Published in: Neural Computing and Applications | Issue 9/2018

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Abstract

In this paper, a delay replacement-based adaptive fault-tolerant control method is proposed for a double inverted pendulum connected by an unknown device. By combining fuzzy approximation and integer backstepping, a new time-delay assumption-independent state feedback decentralized control scheme is developed based on directly replacing the unbounded time-delay argument of fuzzy approximators with the bounded reference signals. Furthermore, all of the two typical types of actuator faults can be compensated for on-line. Compared with the existing results, the time-delay assumptions that need to be test and verify in applications are eliminated, and global bounded stability of the closed-loop system is guaranteed. Simulation results are provided to show the effectiveness of the control approach.

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Literature
1.
go back to reference Yi J, Yubazaki N, Hirota K (2002) A new fuzzy controller for stabilization of parallel-type double inverted pendulum system. Fuzzy Sets Syst 126(1):105–119MathSciNetCrossRefMATH Yi J, Yubazaki N, Hirota K (2002) A new fuzzy controller for stabilization of parallel-type double inverted pendulum system. Fuzzy Sets Syst 126(1):105–119MathSciNetCrossRefMATH
2.
go back to reference Spooner JT, Passino KM (1999) Decentralized adaptive control of nonlinear systems using radial basis neural networks. IEEE Trans Autom Control 44(11):2050–2057MathSciNetCrossRefMATH Spooner JT, Passino KM (1999) Decentralized adaptive control of nonlinear systems using radial basis neural networks. IEEE Trans Autom Control 44(11):2050–2057MathSciNetCrossRefMATH
3.
go back to reference Chen WS, Li JM (2008) Decentralized output-feedback neural control for systems with unknown interconnections. IEEE Trans Syst Man Cybern Part B-Cybern 38(1):258–266CrossRef Chen WS, Li JM (2008) Decentralized output-feedback neural control for systems with unknown interconnections. IEEE Trans Syst Man Cybern Part B-Cybern 38(1):258–266CrossRef
4.
5.
go back to reference Fu YS, Tian ZH, Shi SJ (2003) State feedback stabilization for a class of stochastic time-delay nonlinear systems. IEEE Trans Autom Control 48(2):282–286MathSciNetCrossRefMATH Fu YS, Tian ZH, Shi SJ (2003) State feedback stabilization for a class of stochastic time-delay nonlinear systems. IEEE Trans Autom Control 48(2):282–286MathSciNetCrossRefMATH
6.
go back to reference Guo T, Liu GY (2011) Adaptive fuzzy control for unknown nonlinear time-delay systems with virtual control functions. Int J Control Autom Syst 9(6):1227–1234CrossRef Guo T, Liu GY (2011) Adaptive fuzzy control for unknown nonlinear time-delay systems with virtual control functions. Int J Control Autom Syst 9(6):1227–1234CrossRef
7.
go back to reference Zhou Q, Shi P, Xu SY, Li HY (2013) Adaptive output feedback control for nonlinear time-delay systems by fuzzy approximation approach. IEEE Trans Fuzzy Syst 21(2):301–313CrossRef Zhou Q, Shi P, Xu SY, Li HY (2013) Adaptive output feedback control for nonlinear time-delay systems by fuzzy approximation approach. IEEE Trans Fuzzy Syst 21(2):301–313CrossRef
8.
go back to reference Wu J, Chen WS, Li J (2015) Fuzzy-approximation-based global adaptive control for uncertain strict-feedback systems with a priori known tracking accuracy. Fuzzy Sets Syst 273:1–25MathSciNetCrossRefMATH Wu J, Chen WS, Li J (2015) Fuzzy-approximation-based global adaptive control for uncertain strict-feedback systems with a priori known tracking accuracy. Fuzzy Sets Syst 273:1–25MathSciNetCrossRefMATH
9.
go back to reference Yoo SJ, Park JB (2012) Decentralized adaptive output-feedback control for a class of nonlinear large-scale systems with unknown time-varying delayed interactions. Inf Sci 186(1):222–238MathSciNetCrossRefMATH Yoo SJ, Park JB (2012) Decentralized adaptive output-feedback control for a class of nonlinear large-scale systems with unknown time-varying delayed interactions. Inf Sci 186(1):222–238MathSciNetCrossRefMATH
10.
go back to reference Guo T, Wang AM (2012) Simplified output feedback stabilization for time-delay interconnected systems based on dynamic surface control. Int Rev Comput Softw 7(1):275–282 Guo T, Wang AM (2012) Simplified output feedback stabilization for time-delay interconnected systems based on dynamic surface control. Int Rev Comput Softw 7(1):275–282
11.
go back to reference Yang Y, Yue D, Xue YS (2015) Decentralized adaptive neural output feedback control of a class of large-scale time-delay systems with input saturation. J Frankl Inst-Eng Appl Math 352(5):2129–2151MathSciNetCrossRef Yang Y, Yue D, Xue YS (2015) Decentralized adaptive neural output feedback control of a class of large-scale time-delay systems with input saturation. J Frankl Inst-Eng Appl Math 352(5):2129–2151MathSciNetCrossRef
12.
go back to reference Zhou Q, Shi P, Xu SY, Li HY (2013) Observer-based adaptive neural network control for nonlinear stochastic systems with time delay. IEEE Trans Neural Netw Learn Syst 24(1):71–80CrossRef Zhou Q, Shi P, Xu SY, Li HY (2013) Observer-based adaptive neural network control for nonlinear stochastic systems with time delay. IEEE Trans Neural Netw Learn Syst 24(1):71–80CrossRef
13.
go back to reference Chen B, Liu XP, Liu KF, Lin C (2013) Adaptive fuzzy tracking control of nonlinear MIMO systems with time-varying delays. Fuzzy Sets Syst 217:1–21MathSciNetCrossRefMATH Chen B, Liu XP, Liu KF, Lin C (2013) Adaptive fuzzy tracking control of nonlinear MIMO systems with time-varying delays. Fuzzy Sets Syst 217:1–21MathSciNetCrossRefMATH
14.
go back to reference Chen B, Liu XP, Liu KF, Lin C (2013) Adaptive control for nonlinear MIMO time-delay systems based on fuzzy approximation. Inf Sci 222:576–592MathSciNetCrossRefMATH Chen B, Liu XP, Liu KF, Lin C (2013) Adaptive control for nonlinear MIMO time-delay systems based on fuzzy approximation. Inf Sci 222:576–592MathSciNetCrossRefMATH
15.
go back to reference Zhang X, Lin Y (2015) Adaptive control of nonlinear time-delay systems with application to a two-stage chemical reactor. IEEE Trans Autom Control 60(4):1074–1079MathSciNetCrossRefMATH Zhang X, Lin Y (2015) Adaptive control of nonlinear time-delay systems with application to a two-stage chemical reactor. IEEE Trans Autom Control 60(4):1074–1079MathSciNetCrossRefMATH
16.
go back to reference Ge SS, Hong F, Lee TH (2004) Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients. IEEE Trans Syst Man Cyberns, Part B (Cybern) 34(1):499–516CrossRef Ge SS, Hong F, Lee TH (2004) Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients. IEEE Trans Syst Man Cyberns, Part B (Cybern) 34(1):499–516CrossRef
17.
18.
go back to reference Chen B, Liu XP, Liu KF, Shi P, Lin C (2010) Direct adaptive fuzzy control for nonlinear systems with time-varying delays. Inf Sci 180(5):776–792MathSciNetCrossRefMATH Chen B, Liu XP, Liu KF, Shi P, Lin C (2010) Direct adaptive fuzzy control for nonlinear systems with time-varying delays. Inf Sci 180(5):776–792MathSciNetCrossRefMATH
19.
go back to reference Tong SC, Li Y, Li YM, Liu YJ (2011) Observer-based adaptive fuzzy backstepping control for a class of stochastic nonlinear strict-feedback systems. IEEE Trans Syst Man Cybern, Part B (Cybern) 41(6):1693–1704CrossRef Tong SC, Li Y, Li YM, Liu YJ (2011) Observer-based adaptive fuzzy backstepping control for a class of stochastic nonlinear strict-feedback systems. IEEE Trans Syst Man Cybern, Part B (Cybern) 41(6):1693–1704CrossRef
20.
go back to reference Choi JY, Farrell JA (2001) Adaptive observer backstepping control using neural networks. IEEE Trans Neural Netw 12(5):1103–1112CrossRef Choi JY, Farrell JA (2001) Adaptive observer backstepping control using neural networks. IEEE Trans Neural Netw 12(5):1103–1112CrossRef
21.
go back to reference Wang C, Hill DJ, Ge SS, Chen GR (2006) An ISS-modular approach for adaptive neural control of pure-feedback systems. Automatica 42(5):723–731MathSciNetCrossRefMATH Wang C, Hill DJ, Ge SS, Chen GR (2006) An ISS-modular approach for adaptive neural control of pure-feedback systems. Automatica 42(5):723–731MathSciNetCrossRefMATH
22.
go back to reference Chen WS, Zhang ZQ (2010) Globally stable adaptive backstepping fuzzy control for output-feedback systems with unknown high-frequency gain sign. Fuzzy Sets Syst 161(6):821–836MathSciNetCrossRefMATH Chen WS, Zhang ZQ (2010) Globally stable adaptive backstepping fuzzy control for output-feedback systems with unknown high-frequency gain sign. Fuzzy Sets Syst 161(6):821–836MathSciNetCrossRefMATH
23.
go back to reference Chen WS, Jiao LC, Wu JS (2012) Globally stable adaptive robust tracking control using RBF neural networks as feedforward compensators. Neural Comput Appl 21(2):351–363CrossRef Chen WS, Jiao LC, Wu JS (2012) Globally stable adaptive robust tracking control using RBF neural networks as feedforward compensators. Neural Comput Appl 21(2):351–363CrossRef
24.
go back to reference Huang JT (2012) Global tracking control of strict-feedback systems using neural networks. IEEE Trans Neural Netw Learn Syst 23(11):1714–1725CrossRef Huang JT (2012) Global tracking control of strict-feedback systems using neural networks. IEEE Trans Neural Netw Learn Syst 23(11):1714–1725CrossRef
25.
go back to reference Wu J, Chen WS, Yang FZ, Li J, Zhu Q (2015) Global adaptive neural control for strict-feedback time-delay systems with predefined output accuracy. Inf Sci 301:27–43MathSciNetCrossRefMATH Wu J, Chen WS, Yang FZ, Li J, Zhu Q (2015) Global adaptive neural control for strict-feedback time-delay systems with predefined output accuracy. Inf Sci 301:27–43MathSciNetCrossRefMATH
26.
go back to reference Wang ML, Zhang ZQ (2015) Globally adaptive asymptotic tracking control of nonlinear systems using nonlinearly parameterized fuzzy approximator. J Frankl Inst-Eng Appl Math 352(7):2783–2795MathSciNetCrossRef Wang ML, Zhang ZQ (2015) Globally adaptive asymptotic tracking control of nonlinear systems using nonlinearly parameterized fuzzy approximator. J Frankl Inst-Eng Appl Math 352(7):2783–2795MathSciNetCrossRef
27.
go back to reference Wu J, Chen WS, Zhao D, Li J (2013) Globally stable direct adaptive backstepping NN control for uncertain nonlinear strict-feedback systems. Neurocomputing 122:134–147CrossRef Wu J, Chen WS, Zhao D, Li J (2013) Globally stable direct adaptive backstepping NN control for uncertain nonlinear strict-feedback systems. Neurocomputing 122:134–147CrossRef
28.
go back to reference Wu J, Li J, Chen WS (2014) Semi-globally/globally stable adaptive NN backstepping control for uncertain MIMO systems with tracking accuracy known a priori. J Frankl Inst-Eng Appl Math 351(12):5274–5309MathSciNetCrossRef Wu J, Li J, Chen WS (2014) Semi-globally/globally stable adaptive NN backstepping control for uncertain MIMO systems with tracking accuracy known a priori. J Frankl Inst-Eng Appl Math 351(12):5274–5309MathSciNetCrossRef
29.
go back to reference Huang JT (2015) Global adaptive neural dynamic surface control of strict-feedback systems. Neurocomputing 165:403–413CrossRef Huang JT (2015) Global adaptive neural dynamic surface control of strict-feedback systems. Neurocomputing 165:403–413CrossRef
30.
go back to reference Fu J, Ma RC, Chai TY (2015) Global finite-time stabilization of a class of switched nonlinear systems with the powers of positive odd rational numbers. Automatica 54:360–373MathSciNetCrossRefMATH Fu J, Ma RC, Chai TY (2015) Global finite-time stabilization of a class of switched nonlinear systems with the powers of positive odd rational numbers. Automatica 54:360–373MathSciNetCrossRefMATH
31.
go back to reference Xu B, Yang CG, Pan YP (2015) Global neural dynamic surface tracking control of strict-feedback systems with application to hypersonic flight vehicle. IEEE Trans Neural Netw Learn Syst 26(10):2563–2575MathSciNetCrossRef Xu B, Yang CG, Pan YP (2015) Global neural dynamic surface tracking control of strict-feedback systems with application to hypersonic flight vehicle. IEEE Trans Neural Netw Learn Syst 26(10):2563–2575MathSciNetCrossRef
32.
go back to reference Chen WS, Ge SS, Wu J, Gong MG (2015) Globally stable adaptive backstepping neural network control for uncertain strict-feedback systems with tracking accuracy known a priori. IEEE Trans Neural Netw Learn Syst 26(9):1842–1854MathSciNetCrossRef Chen WS, Ge SS, Wu J, Gong MG (2015) Globally stable adaptive backstepping neural network control for uncertain strict-feedback systems with tracking accuracy known a priori. IEEE Trans Neural Netw Learn Syst 26(9):1842–1854MathSciNetCrossRef
33.
go back to reference Tang XD, Tao G, Joshi SM (2003) Adaptive actuator failure compensation for parametric strict feedback systems and an aircraft application. Automatica 39(11):1975–1982MathSciNetCrossRefMATH Tang XD, Tao G, Joshi SM (2003) Adaptive actuator failure compensation for parametric strict feedback systems and an aircraft application. Automatica 39(11):1975–1982MathSciNetCrossRefMATH
34.
go back to reference Li P, Yang GH (2009) Backstepping adaptive fuzzy control of uncertain nonlinear systems against actuator faults. J Control Theory Appl 7(3):248–256MathSciNetCrossRefMATH Li P, Yang GH (2009) Backstepping adaptive fuzzy control of uncertain nonlinear systems against actuator faults. J Control Theory Appl 7(3):248–256MathSciNetCrossRefMATH
35.
go back to reference Meng LY, Jiang B (2009) Backstepping-based active fault-tolerant control for a class of uncertain SISO nonlinear systems. J Syst Eng Electron 20(6):1263–1270MATH Meng LY, Jiang B (2009) Backstepping-based active fault-tolerant control for a class of uncertain SISO nonlinear systems. J Syst Eng Electron 20(6):1263–1270MATH
36.
go back to reference Wang W, Wen CY (2010) Adaptive actuator failure compensation control of uncertain nonlinear systems with guaranteed transient performance. Automatica 46(12):2082–2091MathSciNetCrossRefMATH Wang W, Wen CY (2010) Adaptive actuator failure compensation control of uncertain nonlinear systems with guaranteed transient performance. Automatica 46(12):2082–2091MathSciNetCrossRefMATH
37.
go back to reference Fan HJ, Liu B, Shen YD, Wang W (2014) Adaptive failure compensation control for uncertain systems with stochastic actuator failures. IEEE Trans Autom Control 59(3):808–814MathSciNetCrossRefMATH Fan HJ, Liu B, Shen YD, Wang W (2014) Adaptive failure compensation control for uncertain systems with stochastic actuator failures. IEEE Trans Autom Control 59(3):808–814MathSciNetCrossRefMATH
38.
go back to reference Fan HJ, Liu B, Wang W, Wen CY (2015) Adaptive fault-tolerant stabilization for nonlinear systems with Markovian jumping actuator failures and stochastic noises. Automatica 51:200–209MathSciNetCrossRefMATH Fan HJ, Liu B, Wang W, Wen CY (2015) Adaptive fault-tolerant stabilization for nonlinear systems with Markovian jumping actuator failures and stochastic noises. Automatica 51:200–209MathSciNetCrossRefMATH
39.
go back to reference Zhang ZQ, Xu SY, Guo Y, Chu YM (2010) Robust adaptive output-feedback control for a class of nonlinear systems with time-varying actuator faults. Int J Adapt Control Signal Process 24(9):743–759MathSciNetCrossRefMATH Zhang ZQ, Xu SY, Guo Y, Chu YM (2010) Robust adaptive output-feedback control for a class of nonlinear systems with time-varying actuator faults. Int J Adapt Control Signal Process 24(9):743–759MathSciNetCrossRefMATH
40.
go back to reference Tong SC, Huo BY, Li YM (2014) Observer-based adaptive decentralized fuzzy fault-tolerant control of nonlinear large-scale systems with actuator failures. IEEE Trans Fuzzy Syst 22(1):1–15CrossRef Tong SC, Huo BY, Li YM (2014) Observer-based adaptive decentralized fuzzy fault-tolerant control of nonlinear large-scale systems with actuator failures. IEEE Trans Fuzzy Syst 22(1):1–15CrossRef
41.
go back to reference Xu YY, Tong SC, Li YM (2015) Adaptive fuzzy decentralised fault-tolerant control for nonlinear large-scale systems with actuator failures and unmodelled dynamics. Int J Syst Sci 46(12):2195–2209MathSciNetCrossRefMATH Xu YY, Tong SC, Li YM (2015) Adaptive fuzzy decentralised fault-tolerant control for nonlinear large-scale systems with actuator failures and unmodelled dynamics. Int J Syst Sci 46(12):2195–2209MathSciNetCrossRefMATH
42.
go back to reference Krstic M, Kokotovic PV, Kanellakopoulos I (1995) Nonlinear and adaptive control design. Wiley, New YorkMATH Krstic M, Kokotovic PV, Kanellakopoulos I (1995) Nonlinear and adaptive control design. Wiley, New YorkMATH
43.
go back to reference Boskovic JD, Mehra RK, Stable multiple model adaptive flight control for accommodation of a large class of control effector failures. In: Proceedings of the 1999 American control conference. IEEE, 2–4 June 1999, vol 3, pp 1920–1924 Boskovic JD, Mehra RK, Stable multiple model adaptive flight control for accommodation of a large class of control effector failures. In: Proceedings of the 1999 American control conference. IEEE, 2–4 June 1999, vol 3, pp 1920–1924
44.
go back to reference Wang LX (1994) Adaptive fuzzy systems and control: design and stability analysis. Prentice-Hall, Englewood Cliffs Wang LX (1994) Adaptive fuzzy systems and control: design and stability analysis. Prentice-Hall, Englewood Cliffs
45.
46.
go back to reference Tang XD, Tao G, Joshi SM (2007) Adaptive actuator failure compensation for nonlinear MIMO systems with an aircraft control application. Automatica 43(11):1869–1883MathSciNetCrossRefMATH Tang XD, Tao G, Joshi SM (2007) Adaptive actuator failure compensation for nonlinear MIMO systems with an aircraft control application. Automatica 43(11):1869–1883MathSciNetCrossRefMATH
47.
Metadata
Title
A new global fuzzy fault-tolerant control for a double inverted pendulum based on time-delay replacement
Authors
Tao Guo
Jing Xiong
Publication date
31-08-2016
Publisher
Springer London
Published in
Neural Computing and Applications / Issue 9/2018
Print ISSN: 0941-0643
Electronic ISSN: 1433-3058
DOI
https://doi.org/10.1007/s00521-016-2576-1

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