© The Institution of Engineering and Technology
In this study, an adaptive neural backstepping control scheme is proposed for a class of strict-feedback non-linear systems with unmodelled dynamics, dynamic disturbances and input saturation. To solve the difficulties from the unmodelled dynamics and input saturation, a dynamic signal and smooth function in non-affine structure subject to the control input signal are introduced, respectively. Radial basis function (RBF) neural networks are used to approximate the packaged unknown non-linearities, and an adaptive neural control approach is developed via backstepping, which guarantees that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded in mean square. The main contributions of this note lie in that a control strategy is provided for a class of strict-feedback non-linear systems with unmodelled dynamics uncertainties and input saturation, and the proposed control scheme does not require any information of the bound of input saturation non-linearity. Simulation results are used to show the effectiveness of the proposed control scheme.
References
-
-
1)
-
31. Apostol, T.M.: ‘Mathematical analysis’ (Addison-Wesley, Reading, MA, 1963).
-
2)
-
23. Tong, S.C., Li, Y.M.: ‘Fuzzy adaptive robust backstepping stabilization for SISO nonlinear systems with unknown virtual control direction’, Inf. Sci., 2010, 180, (23), pp. 4619–4640 (doi: 10.1016/j.ins.2010.07.025).
-
3)
-
28. Perez-Arancibia, N.O., Tsao, T.-C., Gibson, J.S.: ‘Saturation-induced instability and its avoidance in adaptive control of hard disk drives’, IEEE Trans. Control Syst. Technol., 2010, 18, (2), pp. 368–382 (doi: 10.1109/TCST.2009.2018298).
-
4)
-
I. Kanellakopoulos ,
P.V. Kokotovic ,
A.S. Morse
.
Systematic design of adaptive controllers for feedback linearizable systems.
IEEE Trans. Autom. Control
,
11 ,
1241 -
1253
-
5)
-
14. Yin, S., Wang, G., Karimi, H.R.: ‘Data-driven design of robust fault detection system for wind turbines’, Mechatronics, 2014, 24, (4), pp. 298–306 (doi: 10.1016/j.mechatronics.2013.11.009).
-
6)
-
T.S. Li ,
D. Wang ,
G. Feng ,
S.C. Tong
.
A DSC approach to robust adaptive NN tracking control for strict-feedback nonlinear systems.
IEEE Trans. Syst., Man Cybern. B
,
3 ,
915 -
927
-
7)
-
5. Yin, S., Li, X., Gao, H., Kaynak, O.: ‘Data-based techniques focused on modern industry: an overview’, IEEE Trans. Ind. Electron., 2014, .
-
8)
-
38. Qiu, J., Feng, G., Gao, H.: ‘Fuzzy-model-based piecewise H∞ static-output-feedback controller design for networked nonlinear systems’, IEEE Trans. Fuzzy Syst., 2010, 18, (5), pp. 919–934 (doi: 10.1109/TFUZZ.2010.2052259).
-
9)
-
X. Zhao ,
L. Zhang ,
P. Shi ,
M. Liu
.
Stability and stabilization of switched linear systems with mode-dependent average dwell time.
IEEE Trans. Autom. Control
-
10)
-
7. Yin, S., Yang, X., Karimi, H.R.: ‘Data-driven adaptive observer for fault diagnosis’, Math. Probl. Eng., 2012, .
-
11)
-
11. Gao, H.J., Liu, X., Lam, J.: ‘Stability analysis and stabilization for discrete-time fuzzy systems with time-varying delay’, IEEE Trans. Syst. Man Cybern. B, Cybern., 2009, 39, (2), pp. 306–317 (doi: 10.1109/TSMCB.2008.2003449).
-
12)
-
X. Liu ,
A. Jutan ,
S. Rohani
.
Almost disturbance decoupling of multi-input nonlinear systems and application to chemical processes.
Automatica
,
465 -
471
-
13)
-
H. Li ,
H. Liu ,
H. Gao ,
P. Shi
.
Reliable fuzzy control for active suspension systems with actuator delay and faults.
IEEE Trans. Fuzzy Syst.
,
2 ,
342 -
357
-
14)
-
25. Tong, S.C., Liu, C.L., Li, Y.M.: ‘Fuzzy-adaptive decentralized output-feedback control for large-scale nonlinear systems with dynamical uncertainties’, IEEE Trans. Fuzzy Syst., 2010, 18, (5), pp. 845–841 (doi: 10.1109/TFUZZ.2010.2050326).
-
15)
-
18. Chen, B., Liu, K., Liu, X., Shi, P., Lin, C., Zhang, H.: ‘Approximation-based adaptive neural control design for a class of nonlinear systems’, IEEE Trans. Cybern., 2014, 44, (5), pp. 610–619 (doi: 10.1109/TCYB.2013.2263131).
-
16)
-
21. Chen, M., Ge, S.S., How, B.V.E., Choo, Y.S.: ‘Robust adaptive position mooring control for marine vessels’, IEEE Trans. Control Syst. Technol., 2013, 21, (2), pp. 395–409 (doi: 10.1109/TCST.2012.2183676).
-
17)
-
B. Chen ,
X.P. Liu ,
K.F. Liu ,
C. Lin
.
Direct adaptive fuzzy control of nonlinear strict-feedback systems.
Automatica
,
6 ,
1530 -
1535
-
18)
-
21. Wen, C.Y., Zhou, J., Liu, Z.T.: ‘Robust adaptive control of uncertain nonlinear systems in the presence of input saturation and external disturbance’, IEEE Trans. Autom. Control, 2011, 56, (7), pp. 1672–1678 (doi: 10.1109/TAC.2011.2122730).
-
19)
-
31. Liu, Y.J., Chen, L.P., Wen, G.X., Tong, S.C.: ‘Adaptive neural output feedback tracking control for a class of uncertain discrete-time nonlinear systems’, IEEE Trans. Neural Netw., 2011, 22 (7), pp. 1162–1167 (doi: 10.1109/TNN.2011.2146788).
-
20)
-
S.S. Ge ,
C. Wang
.
Direct adaptive NN control of a class of nonlinear systems.
IEEE Trans. Neural Netw.
,
1 ,
214 -
221
-
21)
-
5. Zhao, X., Zhang, L., Shi, P., Karimi, H. R.: ‘Robust control of continuous-time systems with state-dependent uncertainties and its application to electronic circuits’, IEEE Trans. Ind. Electron., 2014, 61, pp. 4161–4170 (doi: 10.1109/TIE.2013.2286568).
-
22)
-
J. Qiu ,
G. Feng ,
J. Yang
.
A new design of delay-dependent robust H∞ filtering for discrete-time T–S fuzzy systems with time-varying delay.
IEEE Trans. Fuzzy Syst.
,
5 ,
1044 -
1058
-
23)
-
27. Tong, S.C., Li, Y.M.: ‘Robust adaptive fuzzy backstepping output feedback tracking control for nonlinear system with dynamic uncertainties’, Sci. China Inf. Sci., 2010, 53, (2), pp. 307–324 (doi: 10.1007/s11432-010-0031-y).
-
24)
-
19. Chen, M., Ge, S.S., Ren, B.B.: ‘Adaptive tracking control of uncertain MIMO nonlinear systems with input saturation’, Automatica, 2011, 47, (3), pp. 452–465 (doi: 10.1016/j.automatica.2011.01.025).
-
25)
-
21. Wang, H., Chen, B., Liu, K.F., Liu, X.P., Lin, C.: ‘Adaptive neural tracking control for a class of nonstrict-feedback stochastic nonlinear systems with unknown backlash-like hysteresis’, IEEE Trans. Neural Netw. Learn. Syst., 2014, 25, (5), pp. 947–958 (doi: 10.1109/TNNLS.2013.2283879).
-
26)
-
R.M. Sanner ,
J.J.-E. Slotine
.
Gaussian network for direct adaptive control.
IEEE Trans. Neural Netw.
,
6 ,
837 -
863
-
27)
-
Z.J. Wu ,
X.J. Xie ,
P. Shi
.
Robust adaptive output-feedback control for nonlinear systems with output unmodeled dynamics.
Int. J. Robust Nonlinear Control
,
1162 -
1187
-
28)
-
H.J. Gao ,
Y. Zhao ,
T.W. Chen
.
H∞ fuzzy control of nonlinear systems under unreliable communication links.
IEEE Trans. Fuzzy Syst.
,
2 ,
265 -
278
-
29)
-
S.C. Tong ,
Y.M. Li ,
P. Shi
.
Fuzzy adaptive backstepping robust control for SISO nonlinear system with dynamic uncertainties.
Inf. Sci.
,
1319 -
1332
-
30)
-
Z.P. Jiang ,
L. Praly
.
Design of robust adaptive controllers for nonlinear systems with dynamic uncertainties.
Automatica
,
825 -
840
-
31)
-
4. Yin, S., Wang, G.: ‘Robust PLS approach for KPI related prediction and diagnosis against outliers and missing data’, Int. J. Syst. Sci., 2014, 45, (7), pp. 1375–1382 (doi: 10.1080/00207721.2014.886136).
-
32)
-
9. Li, H.Y., Jing, X.J., Lam, H.K., Shi, P.: ‘Fuzzy sampled-data control for uncertain vehicle suspension systems’, IEEE Trans. Cybern., 2014, 44, (7), pp. 1111–1126 (doi: 10.1109/TCYB.2013.2279534).
-
33)
-
L. Liu ,
X.J. Xie
.
Output-feedback stabilization for stochastic high-order nonlinear systems with time-varying delay.
Automatica
,
2772 -
2779
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2014.0709
Related content
content/journals/10.1049/iet-cta.2014.0709
pub_keyword,iet_inspecKeyword,pub_concept
6
6