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Erschienen in: Neural Computing and Applications 2/2012

01.03.2012 | Original Article

Globally stable adaptive robust tracking control using RBF neural networks as feedforward compensators

verfasst von: Weisheng Chen, L. C. Jiao, Jianshe Wu

Erschienen in: Neural Computing and Applications | Ausgabe 2/2012

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Abstract

In previous adaptive neural network control schemes, neural networks are usually used as feedback compensators. So, only semi-globally uniformly ultimate boundedness of closed-loop systems can be guaranteed, and no methods are given to determine the neural network approximation domain. However, in this paper, it is showed that if neural networks are used as feedforward compensators instead of feedback ones, then we can ensure the globally uniformly ultimate boundedness of closed-loop systems and determine the neural network approximation domain via the bound of known reference signals. It should be pointed out that this domain is very important for designing the neural network structure, for example, it directly determines the choice of the centers of radial basis function neural networks. Simulation examples are given to illustrate the effectiveness of the proposed control approaches.

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Literatur
1.
Zurück zum Zitat Lewis FL, Yesildirek A, Liu K (1996) Multilayer neural-net robot controller with guaranteed tracking performance. IEEE Trans Neural Netw 7(2):388–399CrossRef Lewis FL, Yesildirek A, Liu K (1996) Multilayer neural-net robot controller with guaranteed tracking performance. IEEE Trans Neural Netw 7(2):388–399CrossRef
2.
Zurück zum Zitat Lewis FL, Jagannathan S, Yesilidrek A (1999) Neural network control of robot manipulators and nonlinear systems. Taylor & Francis, Philadelphia Lewis FL, Jagannathan S, Yesilidrek A (1999) Neural network control of robot manipulators and nonlinear systems. Taylor & Francis, Philadelphia
3.
Zurück zum Zitat Ge SS, Lee TH, Harris CJ (1998) Adaptive neural network control of robot manipulators. World Scientific, London Ge SS, Lee TH, Harris CJ (1998) Adaptive neural network control of robot manipulators. World Scientific, London
4.
5.
Zurück zum Zitat Liu YJ, Tong SC, Wang W (2009) Adaptive fuzzy output tracking control for a class of uncertain nonlinear systems. Fuzzy Sets Syst 160(19):2727–2754MathSciNetCrossRefMATH Liu YJ, Tong SC, Wang W (2009) Adaptive fuzzy output tracking control for a class of uncertain nonlinear systems. Fuzzy Sets Syst 160(19):2727–2754MathSciNetCrossRefMATH
6.
Zurück zum Zitat Chen W, Jiao L, Li J, Li R (2010) Adaptive backstepping fuzzy control for nonlinearly parameterized systems with periodic disturbances. IEEE Trans Fuzzy Syst 18(4):674–685CrossRef Chen W, Jiao L, Li J, Li R (2010) Adaptive backstepping fuzzy control for nonlinearly parameterized systems with periodic disturbances. IEEE Trans Fuzzy Syst 18(4):674–685CrossRef
7.
Zurück zum Zitat Choi JY, Stoev J, Farrell JA (2001) Adaptive observer backstepping control using neural networks. IEEE Trans Neural Netw 12(5):1103–1112CrossRef Choi JY, Stoev J, Farrell JA (2001) Adaptive observer backstepping control using neural networks. IEEE Trans Neural Netw 12(5):1103–1112CrossRef
8.
Zurück zum Zitat Stoev J, Choi JY, Farrell J (2002) Adaptive control for output feedback nonlinear systems in the presence of modeling errors. Automatica 38(10):1761–1767MathSciNetCrossRefMATH Stoev J, Choi JY, Farrell J (2002) Adaptive control for output feedback nonlinear systems in the presence of modeling errors. Automatica 38(10):1761–1767MathSciNetCrossRefMATH
9.
Zurück zum Zitat Chen WS (2009) Adaptive backstepping dynamic surface control for systems with periodic disturbances using neural networks. IET Control Theory Appl 3(10):1383–1394MathSciNetCrossRef Chen WS (2009) Adaptive backstepping dynamic surface control for systems with periodic disturbances using neural networks. IET Control Theory Appl 3(10):1383–1394MathSciNetCrossRef
10.
Zurück zum Zitat Chen W, Tian YP (2009) Neural network approximation for periodically disturbed functions and applications to control design. Neurocomputing 72(16–18):3891–3900CrossRef Chen W, Tian YP (2009) Neural network approximation for periodically disturbed functions and applications to control design. Neurocomputing 72(16–18):3891–3900CrossRef
11.
Zurück zum Zitat Zhang T, Ge SS, Hang CC (2000) Adaptive neural network control for strict-feedback nonlinear systems using backstepping design. Automatica 36(12):1835–1846MathSciNetMATH Zhang T, Ge SS, Hang CC (2000) Adaptive neural network control for strict-feedback nonlinear systems using backstepping design. Automatica 36(12):1835–1846MathSciNetMATH
12.
Zurück zum Zitat Chen W, Jiao L (2010) Adaptive tracking for periodically time-varying and nonlinearly parameterized systems using multilayer neural networks. IEEE Trans Neural Netw 21(2):345–351CrossRef Chen W, Jiao L (2010) Adaptive tracking for periodically time-varying and nonlinearly parameterized systems using multilayer neural networks. IEEE Trans Neural Netw 21(2):345–351CrossRef
13.
Zurück zum Zitat Li J, Chen W, Li JM (2010) Adaptive NN output-feedback decentralized stabilization for a class of large-scale stochastic nonlinear strict-feedback systems. Int J Robust Nonlinear Control. doi:10.1002/rnc.1609 Li J, Chen W, Li JM (2010) Adaptive NN output-feedback decentralized stabilization for a class of large-scale stochastic nonlinear strict-feedback systems. Int J Robust Nonlinear Control. doi:10.​1002/​rnc.​1609
14.
Zurück zum Zitat Chen W, Li W, Miao Q (2010) Backstepping control for periodically time-varying systems using high-order neural network and Fourier series expansion. ISA Trans 49(3):283–292CrossRef Chen W, Li W, Miao Q (2010) Backstepping control for periodically time-varying systems using high-order neural network and Fourier series expansion. ISA Trans 49(3):283–292CrossRef
15.
Zurück zum Zitat 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
16.
Zurück zum Zitat Chen W, Li J (2008) Decentralized output-feedback neural control for systems with unknown interconnections. IEEE Trans Syst Man Cybern Part B 38(1):258–266CrossRef Chen W, Li J (2008) Decentralized output-feedback neural control for systems with unknown interconnections. IEEE Trans Syst Man Cybern Part B 38(1):258–266CrossRef
17.
Zurück zum Zitat Chen W, Jiao L, Li J, Li R (2010) Adaptive NN backstepping output-feedback control for stochastic nonlinear strict-feedback systems with time-varying delays. IEEE Trans Syst Man Cybern Part B 40(3):939–950CrossRef Chen W, Jiao L, Li J, Li R (2010) Adaptive NN backstepping output-feedback control for stochastic nonlinear strict-feedback systems with time-varying delays. IEEE Trans Syst Man Cybern Part B 40(3):939–950CrossRef
18.
Zurück zum Zitat Ge SS, Hong F, Lee TH (2003) Adaptive neural network control of nonlinear systems with unknown time delays. IEEE Trans Automat Control 48(11):2004–2010MathSciNetCrossRef Ge SS, Hong F, Lee TH (2003) Adaptive neural network control of nonlinear systems with unknown time delays. IEEE Trans Automat Control 48(11):2004–2010MathSciNetCrossRef
19.
Zurück zum Zitat Ge SS, Hong F, Lee TH (2004) Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients. IEEE Trans Syst Man Cybern Part B 34(1):499–516MathSciNetCrossRef Ge SS, Hong F, Lee TH (2004) Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients. IEEE Trans Syst Man Cybern Part B 34(1):499–516MathSciNetCrossRef
20.
Zurück zum Zitat Ho DWC, Li J, Niu Y (2005) Adaptive neural control for a class of nonlinearly parametric time-delay systems. IEEE Trans Neural Netw 16(3):625–635CrossRef Ho DWC, Li J, Niu Y (2005) Adaptive neural control for a class of nonlinearly parametric time-delay systems. IEEE Trans Neural Netw 16(3):625–635CrossRef
21.
Zurück zum Zitat Hua C, Guan X, Shi P (2007) Robust output feedback tracking control for time-delay nonlinear systems using neural network. IEEE Trans Neural Netw 18(2):495–505CrossRef Hua C, Guan X, Shi P (2007) Robust output feedback tracking control for time-delay nonlinear systems using neural network. IEEE Trans Neural Netw 18(2):495–505CrossRef
22.
Zurück zum Zitat Hua C, Guan X (2008) Output feedback stabilization for time-delay nonlinear interconnected systems using neural networks. IEEE Trans Neural Netw 19(4):673–688MathSciNetCrossRef Hua C, Guan X (2008) Output feedback stabilization for time-delay nonlinear interconnected systems using neural networks. IEEE Trans Neural Netw 19(4):673–688MathSciNetCrossRef
23.
Zurück zum Zitat Yoo SJ, Park JB (2009) Neural-network-based decentralized adaptive control for a class of large-scale nonlinear systems with unknown time-varying delays. IEEE Trans Syst Man Cybern Part B 39(5):1316–1323CrossRef Yoo SJ, Park JB (2009) Neural-network-based decentralized adaptive control for a class of large-scale nonlinear systems with unknown time-varying delays. IEEE Trans Syst Man Cybern Part B 39(5):1316–1323CrossRef
24.
Zurück zum Zitat Chen B, Liu X, Liu K, Lin C (2009) Novel adaptive neural control design for nonlinear mimo time-delay systems. Automatica 45(6):1554–1560 Chen B, Liu X, Liu K, Lin C (2009) Novel adaptive neural control design for nonlinear mimo time-delay systems. Automatica 45(6):1554–1560
25.
Zurück zum Zitat Ge SS, Li GY, Lee TH (2009) Adaptive NN control for strict-feedback discrete-time nonlinear systems. Automatica 39(5):807–819MathSciNetCrossRef Ge SS, Li GY, Lee TH (2009) Adaptive NN control for strict-feedback discrete-time nonlinear systems. Automatica 39(5):807–819MathSciNetCrossRef
26.
Zurück zum Zitat Ge SS, Li GY, Lee TH (2003) Adaptive NN control for a class of discrete-time nonlinear systems. Int J Control 76(4):334–354MathSciNetCrossRefMATH Ge SS, Li GY, Lee TH (2003) Adaptive NN control for a class of discrete-time nonlinear systems. Int J Control 76(4):334–354MathSciNetCrossRefMATH
27.
Zurück zum Zitat Ge SS, Zhang J, Lee TH (2004) Adaptive neural network control for a class of MIMO nonlinear systems with disturbances in discrete-time. IEEE Trans Syst Man Cybern Part B 34(4):1630–1645CrossRef Ge SS, Zhang J, Lee TH (2004) Adaptive neural network control for a class of MIMO nonlinear systems with disturbances in discrete-time. IEEE Trans Syst Man Cybern Part B 34(4):1630–1645CrossRef
28.
Zurück zum Zitat Zhang J, Ge SS, Lee TH (2005) Output feedback control of a class of discrete MIMO nonlinear systems with triangular form inputs. IEEE Trans Neural Netw 16(6):1491–1503CrossRef Zhang J, Ge SS, Lee TH (2005) Output feedback control of a class of discrete MIMO nonlinear systems with triangular form inputs. IEEE Trans Neural Netw 16(6):1491–1503CrossRef
29.
Zurück zum Zitat Alanis AY, Sanchez EN, Loukianov AG (2007) Discrete-time adaptive backstepping nonlinear control via high-order neural networks. IEEE Trans Neural Netw 18(4):1185–1195CrossRef Alanis AY, Sanchez EN, Loukianov AG (2007) Discrete-time adaptive backstepping nonlinear control via high-order neural networks. IEEE Trans Neural Netw 18(4):1185–1195CrossRef
30.
Zurück zum Zitat Chen W (2009) Comments on ‘Discrete-time adaptive backstepping nonlinear control via high-order neural networks. IEEE Trans Neural Netw 20(5):897–898CrossRef Chen W (2009) Comments on ‘Discrete-time adaptive backstepping nonlinear control via high-order neural networks. IEEE Trans Neural Netw 20(5):897–898CrossRef
31.
Zurück zum Zitat Chen W (2009) Adaptive nn control for discrete-time pure-feedback systems with unknown control direction under amplitude and rate actuator constrains. ISA Trans 48(3):304–311CrossRef Chen W (2009) Adaptive nn control for discrete-time pure-feedback systems with unknown control direction under amplitude and rate actuator constrains. ISA Trans 48(3):304–311CrossRef
32.
Zurück zum Zitat Yang C, Ce SS, Xiang C, Chai T, Lee TH (2008) Output feedback nn control for two classes of discrete-time systems with unknown control directions in a unified approach. IEEE Trans Neural Netw 19(11):1873–1886CrossRef Yang C, Ce SS, Xiang C, Chai T, Lee TH (2008) Output feedback nn control for two classes of discrete-time systems with unknown control directions in a unified approach. IEEE Trans Neural Netw 19(11):1873–1886CrossRef
33.
Zurück zum Zitat Yang C, Ge SS, Lee TH (2009) Output feedback adaptive control of a class of nonlinear discrete-time systems with unknown control directions. Automatica 45(1):270–276MathSciNetCrossRefMATH Yang C, Ge SS, Lee TH (2009) Output feedback adaptive control of a class of nonlinear discrete-time systems with unknown control directions. Automatica 45(1):270–276MathSciNetCrossRefMATH
34.
Zurück zum Zitat Vance J, Jagannathan S (2008) Discrete-time neural network output feedback control of nonlinear discrete-time systems in non-strict form. Automatica 44(4):1020–1027MathSciNetCrossRef Vance J, Jagannathan S (2008) Discrete-time neural network output feedback control of nonlinear discrete-time systems in non-strict form. Automatica 44(4):1020–1027MathSciNetCrossRef
35.
Zurück zum Zitat Jagannathan S (2006) Neural network control of nonlinear discrete-time systems. CRC Press, Boca RatonMATH Jagannathan S (2006) Neural network control of nonlinear discrete-time systems. CRC Press, Boca RatonMATH
36.
Zurück zum Zitat Jagannathan S, Lewis FL (1996) Discrete-time neural net controller for a class of nonlinear dynamical systems. IEEE Trans Automat Control 41(10):1693–1699MathSciNetCrossRefMATH Jagannathan S, Lewis FL (1996) Discrete-time neural net controller for a class of nonlinear dynamical systems. IEEE Trans Automat Control 41(10):1693–1699MathSciNetCrossRefMATH
37.
Zurück zum Zitat Jagannathan S (2001) Control of a class of nonlinear discrete-time system using multilayer neural networks. IEEE Trans Neural Netw 12(5):1113–1120MathSciNetCrossRef Jagannathan S (2001) Control of a class of nonlinear discrete-time system using multilayer neural networks. IEEE Trans Neural Netw 12(5):1113–1120MathSciNetCrossRef
38.
Zurück zum Zitat Jagannathan S, He P (2008) Neural-network-based state-feedback control of a nonlinear discrete-time system in nonstrict feedback form. IEEE Trans Neural Netw 19(12):2073–2087CrossRef Jagannathan S, He P (2008) Neural-network-based state-feedback control of a nonlinear discrete-time system in nonstrict feedback form. IEEE Trans Neural Netw 19(12):2073–2087CrossRef
39.
Zurück zum Zitat Chen FC, Khalil HK (1995) Adaptive control of a class of nonlinear discrete-time systems using neural networks. IEEE Trans Automat Control 72(5):791–807MathSciNetCrossRef Chen FC, Khalil HK (1995) Adaptive control of a class of nonlinear discrete-time systems using neural networks. IEEE Trans Automat Control 72(5):791–807MathSciNetCrossRef
40.
Zurück zum Zitat Ge SS, Huang CC, Lee TH, Zhang T (2001) Stable adaptive neural network control. Kluwer Academic, Norwell Ge SS, Huang CC, Lee TH, Zhang T (2001) Stable adaptive neural network control. Kluwer Academic, Norwell
41.
Zurück zum Zitat Ren X, Lewis FL, Zhang J (2009) Neural network compensation control for mechanical systems with disturbances. Automatica 45(6):1221–1226 Ren X, Lewis FL, Zhang J (2009) Neural network compensation control for mechanical systems with disturbances. Automatica 45(6):1221–1226
42.
Zurück zum Zitat Herrmann G, Lewis FL, Zhang J (2009) Discrete adaptive neural network disturbance feedforward compensation for non-linear disturbances in servo-control applications. Int J Control 82(4):721–740MathSciNetCrossRefMATH Herrmann G, Lewis FL, Zhang J (2009) Discrete adaptive neural network disturbance feedforward compensation for non-linear disturbances in servo-control applications. Int J Control 82(4):721–740MathSciNetCrossRefMATH
43.
Zurück zum Zitat Park J, Sandberg IW (1991) Universal approximation using radial-basis-function networks. Neural Comput 3(2):246–257CrossRef Park J, Sandberg IW (1991) Universal approximation using radial-basis-function networks. Neural Comput 3(2):246–257CrossRef
Metadaten
Titel
Globally stable adaptive robust tracking control using RBF neural networks as feedforward compensators
verfasst von
Weisheng Chen
L. C. Jiao
Jianshe Wu
Publikationsdatum
01.03.2012
Verlag
Springer-Verlag
Erschienen in
Neural Computing and Applications / Ausgabe 2/2012
Print ISSN: 0941-0643
Elektronische ISSN: 1433-3058
DOI
https://doi.org/10.1007/s00521-010-0455-8

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