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Published in: Neural Computing and Applications 7/2018

24-08-2016 | Original Article

Adaptive finite-time control of a class of non-triangular nonlinear systems with input saturation

Authors: Mingjie Cai, Zhengrong Xiang

Published in: Neural Computing and Applications | Issue 7/2018

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Abstract

This paper studies the problem of adaptive neural network finite-time control for a class of non-triangular nonlinear systems with input saturation. Under the assumption that the nonlinearities have strict increasing smooth bounding functions, the backstepping technique can be used to design the state feedback controller and adaptive laws. Neural networks are adopted to approximate some unknown nonlinear functions. With the help of the finite-time Lyapunov stability theorem, it can be proved that the state of the closed-loop system can converge to an arbitrarily small neighborhood of the origin in a finite time. Finally, a numerical simulation example is given to show the effectiveness of the proposed design method.

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Literature
1.
go back to reference Bhat SP, Bernstein DS (1998) Continuous finite-time stabilization of the translational and rotational double integrators. IEEE Trans Autom Control 43(5):678–682MathSciNetCrossRefMATH Bhat SP, Bernstein DS (1998) Continuous finite-time stabilization of the translational and rotational double integrators. IEEE Trans Autom Control 43(5):678–682MathSciNetCrossRefMATH
3.
go back to reference Moulay E, Dambrine M, Yeganefar N, Perruquetti W (2008) Finite-time stability and stabilization of time-delay systems. Syst Control Lett 57(7):561–566MathSciNetCrossRefMATH Moulay E, Dambrine M, Yeganefar N, Perruquetti W (2008) Finite-time stability and stabilization of time-delay systems. Syst Control Lett 57(7):561–566MathSciNetCrossRefMATH
4.
go back to reference Golestani M, Mohammadzaman I, Yazdanpanah MJ (2016) Robust finite-time stabilization of uncertain nonlinear systems based on partial stability. Nonlinear Dyn 85(1):87–96MathSciNetCrossRefMATH Golestani M, Mohammadzaman I, Yazdanpanah MJ (2016) Robust finite-time stabilization of uncertain nonlinear systems based on partial stability. Nonlinear Dyn 85(1):87–96MathSciNetCrossRefMATH
5.
go back to reference Hoagg J, Bernstein D (2007) Lyapunov-stable adaptive stabilization of non-linear time-varying systems with matched uncertainty. Int J Control 80(6):872–884MathSciNetCrossRefMATH Hoagg J, Bernstein D (2007) Lyapunov-stable adaptive stabilization of non-linear time-varying systems with matched uncertainty. Int J Control 80(6):872–884MathSciNetCrossRefMATH
6.
go back to reference Li F, Wu L, Shi P, Lim CC (2015) State estimation and sliding mode control for semi-Markovian jump systems with mismatched uncertainties. Automatica 51:385–393MathSciNetCrossRefMATH Li F, Wu L, Shi P, Lim CC (2015) State estimation and sliding mode control for semi-Markovian jump systems with mismatched uncertainties. Automatica 51:385–393MathSciNetCrossRefMATH
7.
go back to reference Arefi MM, Jahedmotlagh MR, Karimi HR (2015) Adaptive neural stabilizing controller for a class of mismatched uncertain nonlinear systems by state and output feedback. IEEE Trans Cybern 45(8):1587–1596CrossRef Arefi MM, Jahedmotlagh MR, Karimi HR (2015) Adaptive neural stabilizing controller for a class of mismatched uncertain nonlinear systems by state and output feedback. IEEE Trans Cybern 45(8):1587–1596CrossRef
8.
go back to reference Arefi MM, Zarei J, Karimi HR (2014) Adaptive output feedback neural network control of uncertain non-affine systems with unknown control direction. J Frankl Inst 351(8):4302–4316MathSciNetCrossRefMATH Arefi MM, Zarei J, Karimi HR (2014) Adaptive output feedback neural network control of uncertain non-affine systems with unknown control direction. J Frankl Inst 351(8):4302–4316MathSciNetCrossRefMATH
9.
10.
go back to reference Zhao L, Pawlus W, Karimi HR, Robbersmyr KG (2014) Data-based modeling of vehicle crash using adaptive neural-fuzzy inference system. IEEE/ASME Trans Mechatron 19(2):684–696CrossRef Zhao L, Pawlus W, Karimi HR, Robbersmyr KG (2014) Data-based modeling of vehicle crash using adaptive neural-fuzzy inference system. IEEE/ASME Trans Mechatron 19(2):684–696CrossRef
11.
go back to reference Liu H, Zhang T (2013) Neural network-based robust finite-time control for robotic manipulators considering actuator dynamics. Robot Comput Integr Manuf 29(2):301–308CrossRef Liu H, Zhang T (2013) Neural network-based robust finite-time control for robotic manipulators considering actuator dynamics. Robot Comput Integr Manuf 29(2):301–308CrossRef
12.
go back to reference Liu H, Zhang T (2014) Adaptive neural network finite-time control for uncertain robotic manipulators. J Intell Robot Syst 75(3–4):363–377CrossRef Liu H, Zhang T (2014) Adaptive neural network finite-time control for uncertain robotic manipulators. J Intell Robot Syst 75(3–4):363–377CrossRef
13.
go back to reference Chen Q, Ren X, Na J, Zheng D (2016) Adaptive robust finite-time neural control of uncertain PMSM servo system with nonlinear dead zone. Neural Comput Appl. doi:10.1007/s00521-016-2260-5 Chen Q, Ren X, Na J, Zheng D (2016) Adaptive robust finite-time neural control of uncertain PMSM servo system with nonlinear dead zone. Neural Comput Appl. doi:10.​1007/​s00521-016-2260-5
14.
go back to reference Huang J, Wen C, Wang W, Song YD (2014) Adaptive finite-time consensus control of a group of uncertain nonlinear mechanical systems. Automatica 51:292–301MathSciNetCrossRefMATH Huang J, Wen C, Wang W, Song YD (2014) Adaptive finite-time consensus control of a group of uncertain nonlinear mechanical systems. Automatica 51:292–301MathSciNetCrossRefMATH
15.
go back to reference Zhu Z, Xia Y, Fu M (2011) Attitude stabilization of rigid spacecraft with finite-time convergence. Int J Robust Nonlinear Control 21(6):686–702MathSciNetCrossRefMATH Zhu Z, Xia Y, Fu M (2011) Attitude stabilization of rigid spacecraft with finite-time convergence. Int J Robust Nonlinear Control 21(6):686–702MathSciNetCrossRefMATH
16.
go back to reference Kanelakopoulos I, Kokotovic PV, Morse AS (1991) Systematic design of adaptive controller for feedback linearizable systems. IEEE Trans Autom Control 36(11):1241–1253MathSciNetCrossRefMATH Kanelakopoulos I, Kokotovic PV, Morse AS (1991) Systematic design of adaptive controller for feedback linearizable systems. IEEE Trans Autom Control 36(11):1241–1253MathSciNetCrossRefMATH
17.
go back to reference Lin W, Qian C (2000) Adding one power integrator: a tool for global stabilization of high-order lower-triangular systems. Syst Control Lett 39(5):339–351MathSciNetCrossRefMATH Lin W, Qian C (2000) Adding one power integrator: a tool for global stabilization of high-order lower-triangular systems. Syst Control Lett 39(5):339–351MathSciNetCrossRefMATH
18.
go back to reference Fang Y, Hou S, Fei J (2015) Harmonic suppression of three-phase active power filter using backstepping approach. Int J Innov Comput Inf Control 11(2):497–507 Fang Y, Hou S, Fei J (2015) Harmonic suppression of three-phase active power filter using backstepping approach. Int J Innov Comput Inf Control 11(2):497–507
19.
go back to reference Qian C, Li J (2005) Global finite-time stabilization by output feedback for planar systems without observable linearization. IEEE Trans Autom Control 50(6):885–890MathSciNetCrossRefMATH Qian C, Li J (2005) Global finite-time stabilization by output feedback for planar systems without observable linearization. IEEE Trans Autom Control 50(6):885–890MathSciNetCrossRefMATH
20.
go back to reference Hong Y, Jiang ZP (2006) Finite-time stabilization of nonlinear systems with parametric and dynamic uncertainties. IEEE Trans Autom Control 51(12):1950–1956MathSciNetCrossRefMATH Hong Y, Jiang ZP (2006) Finite-time stabilization of nonlinear systems with parametric and dynamic uncertainties. IEEE Trans Autom Control 51(12):1950–1956MathSciNetCrossRefMATH
21.
go back to reference Cheng Y, Du H, He Y, Jia R (2014) Finite-time tracking control for a class of high-order nonlinear systems and its applications. Nonlinear Dyn 76(2):1133–1140MathSciNetCrossRefMATH Cheng Y, Du H, He Y, Jia R (2014) Finite-time tracking control for a class of high-order nonlinear systems and its applications. Nonlinear Dyn 76(2):1133–1140MathSciNetCrossRefMATH
22.
go back to reference Cai M, Xiang Z (2015) Adaptive neural finite-time control for a class of switched nonlinear systems. Neurocomputing 155:177–185CrossRef Cai M, Xiang Z (2015) Adaptive neural finite-time control for a class of switched nonlinear systems. Neurocomputing 155:177–185CrossRef
23.
go back to reference Huang J, Wen C, Wang W, Song YD (2016) Design of adaptive finite-time controllers for nonlinear uncertain systems based on given transient specifications. Automatica 69:395–404MathSciNetCrossRefMATH Huang J, Wen C, Wang W, Song YD (2016) Design of adaptive finite-time controllers for nonlinear uncertain systems based on given transient specifications. Automatica 69:395–404MathSciNetCrossRefMATH
24.
go back to reference Hong Y, Wang J, Cheng D (2006) Adaptive finite-time control of nonlinear systems with parametric uncertainty. IEEE Trans Autom Control 51(5):858–862MathSciNetCrossRefMATH Hong Y, Wang J, Cheng D (2006) Adaptive finite-time control of nonlinear systems with parametric uncertainty. IEEE Trans Autom Control 51(5):858–862MathSciNetCrossRefMATH
25.
go back to reference Sun ZY, Xue LR, Zhang K (2015) A new approach to finite-time adaptive stabilization of high-order uncertain nonlinear system. Automatica 58:60–66MathSciNetCrossRefMATH Sun ZY, Xue LR, Zhang K (2015) A new approach to finite-time adaptive stabilization of high-order uncertain nonlinear system. Automatica 58:60–66MathSciNetCrossRefMATH
26.
go back to reference Li J, Qian C, Ding S (2010) Global finite-time stabilisation by output feedback for a class of uncertain nonlinear systems. Int J Control 83:2241–2252MathSciNetCrossRefMATH Li J, Qian C, Ding S (2010) Global finite-time stabilisation by output feedback for a class of uncertain nonlinear systems. Int J Control 83:2241–2252MathSciNetCrossRefMATH
27.
go back to reference Liang YJ, Ma R, Wang M, Fu J (2015) Global finite-time stabilisation of a class of switched nonlinear systems. Int J Syst Sci 46(16):2897–2904MathSciNetCrossRefMATH Liang YJ, Ma R, Wang M, Fu J (2015) Global finite-time stabilisation of a class of switched nonlinear systems. Int J Syst Sci 46(16):2897–2904MathSciNetCrossRefMATH
28.
go back to reference Yao B, Tomizuka M (1997) Adaptive robust control of SISO nonlinear systems in a semi-strict feedback form. Automatica 33(5):893–900MathSciNetCrossRefMATH Yao B, Tomizuka M (1997) Adaptive robust control of SISO nonlinear systems in a semi-strict feedback form. Automatica 33(5):893–900MathSciNetCrossRefMATH
29.
go back to reference Liu Y (2014) Global finite-time stabilization via time-varying feedback for uncertain nonlinear systems. SIAM J Control Optim 52(3):1886–1913MathSciNetCrossRefMATH Liu Y (2014) Global finite-time stabilization via time-varying feedback for uncertain nonlinear systems. SIAM J Control Optim 52(3):1886–1913MathSciNetCrossRefMATH
30.
go back to reference Ma R, Liu Y, Zhao S, Fu J (2015) Finite-time stabilization of a class of output-constrained nonlinear systems. J Frankl Inst 352(12):5968–5984MathSciNetCrossRef Ma R, Liu Y, Zhao S, Fu J (2015) Finite-time stabilization of a class of output-constrained nonlinear systems. J Frankl Inst 352(12):5968–5984MathSciNetCrossRef
31.
go back to reference Wang H, Liu X, Liu K, Karimi HR (2015) Approximation-based adaptive fuzzy tracking control for a class of non-strict-feedback stochastic nonlinear time-delay systems. IEEE Trans Fuzzy Syst 23(5):1746–1760CrossRef Wang H, Liu X, Liu K, Karimi HR (2015) Approximation-based adaptive fuzzy tracking control for a class of non-strict-feedback stochastic nonlinear time-delay systems. IEEE Trans Fuzzy Syst 23(5):1746–1760CrossRef
32.
go back to reference Zhao X, Yang H, Karimi HR, Zhu Y (2016) Adaptive neural control of MIMO nonstrict-feedback nonlinear systems with time delay. IEEE Trans Cybern 46(6):1337–1349CrossRef Zhao X, Yang H, Karimi HR, Zhu Y (2016) Adaptive neural control of MIMO nonstrict-feedback nonlinear systems with time delay. IEEE Trans Cybern 46(6):1337–1349CrossRef
33.
go back to reference Hu Q, Huo X, Xiao B (2013) Reaction wheel fault tolerant control for spacecraft attitude stabilization with finite-time convergence. Int J Robust Nonlinear Control 23(15):1737–1752MathSciNetMATH Hu Q, Huo X, Xiao B (2013) Reaction wheel fault tolerant control for spacecraft attitude stabilization with finite-time convergence. Int J Robust Nonlinear Control 23(15):1737–1752MathSciNetMATH
34.
go back to reference Lyu J, Qin J, Gao D, Liu Q (2015) Consensus for constrained multi-agent systems with input saturation. Int J Robust Nonlinear Control 17(4):184–192MATH Lyu J, Qin J, Gao D, Liu Q (2015) Consensus for constrained multi-agent systems with input saturation. Int J Robust Nonlinear Control 17(4):184–192MATH
35.
go back to reference Zhang B, Jia Y, Matsuno F (2014) Finite-time observers for multi-agent systems without velocity measurements and with input saturations. Syst Control Lett 68(1):86–94MathSciNetCrossRefMATH Zhang B, Jia Y, Matsuno F (2014) Finite-time observers for multi-agent systems without velocity measurements and with input saturations. Syst Control Lett 68(1):86–94MathSciNetCrossRefMATH
36.
go back to reference Qian C, Wei L (2001) Non-Lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization. Syst Control Lett 42(3):185–200MathSciNetCrossRef Qian C, Wei L (2001) Non-Lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization. Syst Control Lett 42(3):185–200MathSciNetCrossRef
37.
go back to reference Qian C, Li J (2006) Global output feedback stabilization of upper-triangular nonlinear systems using a homogeneous domination approach. Int J Robust Nonlinear Control 16(9):441–463MathSciNetCrossRefMATH Qian C, Li J (2006) Global output feedback stabilization of upper-triangular nonlinear systems using a homogeneous domination approach. Int J Robust Nonlinear Control 16(9):441–463MathSciNetCrossRefMATH
38.
go back to reference Zhu Z, Xia Y, Fu M (2011) Attitude stabilization of rigid spacecraft with finite-time convergence. Int J Robust Nonlinear Control 21:686–702MathSciNetCrossRefMATH Zhu Z, Xia Y, Fu M (2011) Attitude stabilization of rigid spacecraft with finite-time convergence. Int J Robust Nonlinear Control 21:686–702MathSciNetCrossRefMATH
Metadata
Title
Adaptive finite-time control of a class of non-triangular nonlinear systems with input saturation
Authors
Mingjie Cai
Zhengrong Xiang
Publication date
24-08-2016
Publisher
Springer London
Published in
Neural Computing and Applications / Issue 7/2018
Print ISSN: 0941-0643
Electronic ISSN: 1433-3058
DOI
https://doi.org/10.1007/s00521-016-2540-0

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