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Published in: Neural Computing and Applications 10/2019

02-04-2018 | Original Article

Synchronization of single-degree-of-freedom oscillators via neural network based on fixed-time terminal sliding mode control scheme

Authors: Haibin Sun, Linlin Hou, Chaojie Li

Published in: Neural Computing and Applications | Issue 10/2019

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Abstract

In this paper, the synchronization problem is investigated for two single-degree-of-freedom oscillators via neural network based on fixed-time terminal sliding mode control. First, a fixed-time terminal sliding mode is constructed. Then, in order to deal with the unknown function in master system, the neural network technique is introduced. Combining fixed-time terminal sliding mode surface and adaptive control scheme plus neural network technique, an adaptive fixed-time terminal sliding mode controller is presented. The stability of the closed-loop system is analyzed. Finally, simulation results are provided to demonstrate the effectiveness of the proposed two control strategies.

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Literature
1.
go back to reference Chung SJ, Slotine JJE (2009) Cooperative robot control and concurrent synchronization of Lagrangian systems. IEEE Trans Rob 25(3):686–700CrossRef Chung SJ, Slotine JJE (2009) Cooperative robot control and concurrent synchronization of Lagrangian systems. IEEE Trans Rob 25(3):686–700CrossRef
2.
go back to reference Du HB, Li SH (2014) Attitude synchronization control for a group of flexible spacecraft. Automatica 50(2):646–651MathSciNetCrossRef Du HB, Li SH (2014) Attitude synchronization control for a group of flexible spacecraft. Automatica 50(2):646–651MathSciNetCrossRef
3.
go back to reference Zhang Z, Shen H, Li J (2011) Adaptive stabilization of uncertain unified chaotic systems with nonlinear input. Appl Math Comput 218(8):4260–4267MathSciNetMATH Zhang Z, Shen H, Li J (2011) Adaptive stabilization of uncertain unified chaotic systems with nonlinear input. Appl Math Comput 218(8):4260–4267MathSciNetMATH
4.
go back to reference Jia Q (2007) Adaptive control and synchronization of a new hyperchaotic system with unknown parameters. Phys Lett A 362(5–6):424–429CrossRef Jia Q (2007) Adaptive control and synchronization of a new hyperchaotic system with unknown parameters. Phys Lett A 362(5–6):424–429CrossRef
5.
go back to reference Li R, Xu W, Li S (2009) Anti-synchronization on autonomous and non-autonomous chaotic systems via adaptive feedback control. Chaos Solitons Fractals 40(3):1288–1296MathSciNetCrossRef Li R, Xu W, Li S (2009) Anti-synchronization on autonomous and non-autonomous chaotic systems via adaptive feedback control. Chaos Solitons Fractals 40(3):1288–1296MathSciNetCrossRef
6.
go back to reference Li HQ, Liao XF, Li CD, Li CJ (2011) Chaos control and synchronization via a novel chatter free sliding mode control strategy. Neurocomputing 74(17):3212–3222CrossRef Li HQ, Liao XF, Li CD, Li CJ (2011) Chaos control and synchronization via a novel chatter free sliding mode control strategy. Neurocomputing 74(17):3212–3222CrossRef
7.
go back to reference Li HQ, Liao XF, Chen G, Hill DJ, Dong ZY, Huang TW (2015) Event-triggered asynchronous intermittent communication strategy for synchronization in complex dynamical networks. Neural Netw 66:1–10CrossRef Li HQ, Liao XF, Chen G, Hill DJ, Dong ZY, Huang TW (2015) Event-triggered asynchronous intermittent communication strategy for synchronization in complex dynamical networks. Neural Netw 66:1–10CrossRef
8.
go back to reference Li CJ, Gao DY, Liu C, Chen G (2014) Impulsive control for synchronizing delayed discrete complex networks with switching topology. Neural Comput Appl 24(1):59–68CrossRef Li CJ, Gao DY, Liu C, Chen G (2014) Impulsive control for synchronizing delayed discrete complex networks with switching topology. Neural Comput Appl 24(1):59–68CrossRef
10.
go back to reference Li CJ, Yu XH, Yu WW, Huang TW, Liu ZW (2016) Distributed event-triggered scheme for economic dispatch in smart grids. IEEE Trans Ind Inf 12(5):1775–1785CrossRef Li CJ, Yu XH, Yu WW, Huang TW, Liu ZW (2016) Distributed event-triggered scheme for economic dispatch in smart grids. IEEE Trans Ind Inf 12(5):1775–1785CrossRef
11.
go back to reference Lei Y, Xu W, Shen J, Fang T (2006) Global synchronization of two parametrically excited systems using active control. Chaos Solitons Fractals 28(2):428–436MathSciNetCrossRef Lei Y, Xu W, Shen J, Fang T (2006) Global synchronization of two parametrically excited systems using active control. Chaos Solitons Fractals 28(2):428–436MathSciNetCrossRef
12.
go back to reference Wu XF, Cai JP, Wang MH (2008) Global chaos synchronization of the parametrically excited Duffing oscillators by linear state error feedback control. Chaos Solitons Fractals 36(1):121–128MathSciNetCrossRef Wu XF, Cai JP, Wang MH (2008) Global chaos synchronization of the parametrically excited Duffing oscillators by linear state error feedback control. Chaos Solitons Fractals 36(1):121–128MathSciNetCrossRef
13.
go back to reference Lei Y, Yung KL, Xu Y (2010) Chaos synchronization and parameter estimation of single-degree-of-freedom oscillators via adaptive control. J Sound Vib 329(8):973–979CrossRef Lei Y, Yung KL, Xu Y (2010) Chaos synchronization and parameter estimation of single-degree-of-freedom oscillators via adaptive control. J Sound Vib 329(8):973–979CrossRef
14.
go back to reference Zhang Z, Wang Y, Du Z (2012) Adaptive synchronization of single-degree-of-freedom oscillators with unknown parameters. Appl Math Comput 218(12):6833–6840MathSciNetMATH Zhang Z, Wang Y, Du Z (2012) Adaptive synchronization of single-degree-of-freedom oscillators with unknown parameters. Appl Math Comput 218(12):6833–6840MathSciNetMATH
15.
go back to reference Yan JJ, Hung ML, Liao TL (2006) Adaptive sliding mode control for synchronization of chaotic gyros with fully unknown parameters. J Sound Vib 298(1–2):298–306MathSciNetCrossRef Yan JJ, Hung ML, Liao TL (2006) Adaptive sliding mode control for synchronization of chaotic gyros with fully unknown parameters. J Sound Vib 298(1–2):298–306MathSciNetCrossRef
16.
17.
go back to reference Haibo Du, Xinghuo Yu, Michael Z.Q. Chen, Shihua Li, (2016) Chattering-free discrete-time sliding mode control. Automatica 68:87-91MathSciNetCrossRef Haibo Du, Xinghuo Yu, Michael Z.Q. Chen, Shihua Li, (2016) Chattering-free discrete-time sliding mode control. Automatica 68:87-91MathSciNetCrossRef
18.
go back to reference Du HB, Wen GH, Cheng YY, He YG, Jia RT (2017) Distributed finite-time cooperative control of multiple high-order nonholonomic mobile robots. IEEE Trans Neural Netw Learn Syst 28(12):2998–3006MathSciNetCrossRef Du HB, Wen GH, Cheng YY, He YG, Jia RT (2017) Distributed finite-time cooperative control of multiple high-order nonholonomic mobile robots. IEEE Trans Neural Netw Learn Syst 28(12):2998–3006MathSciNetCrossRef
19.
go back to reference Du HB, Wen GH, Yu XH, Li SH, Chen MZQ (2015) Finite-time consensus of multiple nonholonomic chained-form systems based on recursive distributed observer. Automatica 62(12):236–242MathSciNetCrossRef Du HB, Wen GH, Yu XH, Li SH, Chen MZQ (2015) Finite-time consensus of multiple nonholonomic chained-form systems based on recursive distributed observer. Automatica 62(12):236–242MathSciNetCrossRef
20.
go back to reference Du HB, He YG, Cheng YY (2014) Finite-time synchronization of a class of second-order nonlinear multi-agent systems using output feedback control. IEEE Trans Circuits Syst I Regul Pap 61(6):1778–1788CrossRef Du HB, He YG, Cheng YY (2014) Finite-time synchronization of a class of second-order nonlinear multi-agent systems using output feedback control. IEEE Trans Circuits Syst I Regul Pap 61(6):1778–1788CrossRef
21.
go back to reference Sun H, Hou L, Zong G (2016) Continuous finite time control for static var compensator with mismatched disturbances. Nonlinear Dyn 85(4):2159–2169CrossRef Sun H, Hou L, Zong G (2016) Continuous finite time control for static var compensator with mismatched disturbances. Nonlinear Dyn 85(4):2159–2169CrossRef
22.
go back to reference Aghababa MP, Khanmohammadi S, Alizadeh G (2011) Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique. Appl Math Model 35(6):3080–3091MathSciNetCrossRef Aghababa MP, Khanmohammadi S, Alizadeh G (2011) Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique. Appl Math Model 35(6):3080–3091MathSciNetCrossRef
23.
24.
go back to reference Filippov AF (1988) Differential equations with discontinuous right-hand sides. Kluwer Academic, New YorkCrossRef Filippov AF (1988) Differential equations with discontinuous right-hand sides. Kluwer Academic, New YorkCrossRef
25.
go back to reference Polyakov A (2012) Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans Autom Control 57(8):2106–2110MathSciNetCrossRef Polyakov A (2012) Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans Autom Control 57(8):2106–2110MathSciNetCrossRef
26.
go back to reference Zuo ZY (2015) Non-singular fixed-time terminal sliding mode control of non-linear systems. IET Control Theory Appl 9(4):545–552MathSciNetCrossRef Zuo ZY (2015) Non-singular fixed-time terminal sliding mode control of non-linear systems. IET Control Theory Appl 9(4):545–552MathSciNetCrossRef
27.
go back to reference Ni JK, Liu L, Liu CX, Hu XY, Li SL (2017) Fast fixed-time nonsingular terminal sliding mode control and its application to chaos suppression in power system. IEEE Trans Circuits Syst II Express Briefs 64(2):151–155CrossRef Ni JK, Liu L, Liu CX, Hu XY, Li SL (2017) Fast fixed-time nonsingular terminal sliding mode control and its application to chaos suppression in power system. IEEE Trans Circuits Syst II Express Briefs 64(2):151–155CrossRef
28.
go back to reference 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
29.
go back to reference Sanner RM, Slotine JJ (1992) Gaussian networks for direct adaptive control. IEEE Trans Neural Netw 3(6):837–863CrossRef Sanner RM, Slotine JJ (1992) Gaussian networks for direct adaptive control. IEEE Trans Neural Netw 3(6):837–863CrossRef
30.
go back to reference Sun H, Guo L (2017) Neural network-based DOBC for a class of nonlinear systems with unmatched disturbances. IEEE Trans Neural Netw Learn Syst 28(2):482–489MathSciNetCrossRef Sun H, Guo L (2017) Neural network-based DOBC for a class of nonlinear systems with unmatched disturbances. IEEE Trans Neural Netw Learn Syst 28(2):482–489MathSciNetCrossRef
31.
go back to reference Li CJ, Yu XH, Huang TW, Chen G, He X (2016) A generalized Hopfield network for nonsmooth constrained convex optimization: Lie derivative approach. IEEE Trans Neural Netw Learn Syst 27(2):308–321MathSciNetCrossRef Li CJ, Yu XH, Huang TW, Chen G, He X (2016) A generalized Hopfield network for nonsmooth constrained convex optimization: Lie derivative approach. IEEE Trans Neural Netw Learn Syst 27(2):308–321MathSciNetCrossRef
32.
go back to reference Bhat SP, Bernstein DS (1995) Lyapunov analysis of finite-time differential equations. In: Proceedings of the American control conference, 1831–1832 Bhat SP, Bernstein DS (1995) Lyapunov analysis of finite-time differential equations. In: Proceedings of the American control conference, 1831–1832
33.
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):678–682MathSciNetCrossRef Bhat SP, Bernstein DS (1998) Continuous finite-time stabilization of the translational and rotational double integrators. IEEE Trans Autom Control 43(5):678–682MathSciNetCrossRef
34.
go back to reference Feng Y, Yu X, Man Z (2002) Non-singular terminal sliding mode control of rigid manipulators. Automatica 28(11):2159–2167MathSciNetCrossRef Feng Y, Yu X, Man Z (2002) Non-singular terminal sliding mode control of rigid manipulators. Automatica 28(11):2159–2167MathSciNetCrossRef
35.
go back to reference Sun HB, Li SH, Sun CY (2013) Finite time integral sliding mode control of hypersonic vehicles. Nonlinear Dyn 73(1–2):229–244MathSciNetCrossRef Sun HB, Li SH, Sun CY (2013) Finite time integral sliding mode control of hypersonic vehicles. Nonlinear Dyn 73(1–2):229–244MathSciNetCrossRef
36.
go back to reference Li YK, Sun HB, Zong GD, Hou LL (2017) Composite anti-disturbance resilient control for Markovian jump nonlinear systems with partly unknown transition probabilities and multiple disturbances. Int J Robust Nonlinear Control 27(14):2323–2337MathSciNetCrossRef Li YK, Sun HB, Zong GD, Hou LL (2017) Composite anti-disturbance resilient control for Markovian jump nonlinear systems with partly unknown transition probabilities and multiple disturbances. Int J Robust Nonlinear Control 27(14):2323–2337MathSciNetCrossRef
37.
go back to reference Xu B, Sun FC (2018) Composite intelligent learning control of strict feedback systems with disturbance. IEEE Trans Cybern 48(2):730–741CrossRef Xu B, Sun FC (2018) Composite intelligent learning control of strict feedback systems with disturbance. IEEE Trans Cybern 48(2):730–741CrossRef
38.
go back to reference Sun HB, Li YK, Zong GD, Hou LL (2018) Disturbance attenuation and rejection for stochastic Markovian jump system with partially known transition probabilities. Automatica 89:349–357MathSciNetCrossRef Sun HB, Li YK, Zong GD, Hou LL (2018) Disturbance attenuation and rejection for stochastic Markovian jump system with partially known transition probabilities. Automatica 89:349–357MathSciNetCrossRef
Metadata
Title
Synchronization of single-degree-of-freedom oscillators via neural network based on fixed-time terminal sliding mode control scheme
Authors
Haibin Sun
Linlin Hou
Chaojie Li
Publication date
02-04-2018
Publisher
Springer London
Published in
Neural Computing and Applications / Issue 10/2019
Print ISSN: 0941-0643
Electronic ISSN: 1433-3058
DOI
https://doi.org/10.1007/s00521-018-3445-x

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