A novel output-feedback controller for uncertain single-input single-output (SISO) nonaffine nonlinear systems is proposed using high-order sliding mode (HOSM) observer, which is a robust exact finite-time convergent differentiator. The proposed controller utilizes (n + 1)th-order HOSM observer to cancel the uncertainty and disturbance where n is the relative degree of the controlled system. As a result, the control law has an extremely simple form of linear in the differentiator states. It is required no separate sliding-mode controller or universal approximators such as neural networks (NNs) or fuzzy logic systems (FLSs) that are adaptively tuned online. The proposed controller guarantees finite time stability of the output tracking error.
Issue Section:
Technical Brief
References
1.
Wang
, W.-Y.
, Chan
, M.-L.
, Hsu
, C.-C. J.
, and Lee
, T.-T.
, 2002
, “H∞ Tracking-Based Sliding Mode Control for Uncertain Nonlinear Systems via an Adaptive Fuzzy-Neural Approach
,” IEEE Trans. Syst., Man, Cybern.-Part B
, 32
(4
), pp. 483
–492
.2.
Park
, J.-H.
, Huh
, S.-H.
, Kim
, S.-H.
, Seo
, S.-J.
, and Park
, G.-T.
, 2005
, “Direct Adaptive Controller for Nonaffine Nonlinear Systems Using Self-Structuring Neural Networks
,” IEEE Trans. Neural Networks
, 16
(2
), pp. 414
–422
.3.
Park
, J.-H.
, Park
, G.-T.
, Kim
, S.-H.
, and Moon
, C.-J.
, 2005
, “Direct Adaptive Self-Structuring Fuzzy Controller for Nonaffine Nonlinear Systems
,” Fuzzy Sets Syst.
, 153
(3
), pp. 429
–445
.4.
Park
, J.-H.
, Kim
, S.-H.
, and Moon
, C.-J.
, 2009
, “Adaptive Neural Control for Strict-Feedback Nonlinear Systems Without Backstepping
,” IEEE Trans. Neural Networks
, 20
(7
), pp. 1204
–1209
.5.
Na
, J.
, Ren
, X.
, and Zheng
, D.
, 2013
, “Adaptive Control for Nonlinear Pure-Feedback Systems With High-Order Sliding Mode Observer
,” IEEE Trans. Neural Networks Learn. Syst.
, 24
(3
), pp. 370
–382
.6.
Shen
, Q.
, Zhang
, T.
, and Lim
, C.-C.
, 2014
, “Novel Neural Control for a Class of Uncertain Pure-Feedback Systems
,” IEEE Trans. Neural Networks Learn. Syst.
, 86
(5
), pp. 912
–922
.7.
Wang
, H.
, Chen
, B.
, Lin
, C.
, and Sun
, Y.
, 2016
, “Observer-Based Adaptive Neural Control for a Class of Nonlinear Pure-Feedback Systems
,” Neurocomputing
, 171
, pp. 1517
–1523
.8.
Levant
, A.
, 2003
, “Higher-Order Sliding Modes, Differentiation and Output-Feedback Control
,” Int. J. Control
, 76
(9–10
), pp. 924
–941
.9.
Levant
, A.
, 2005
, “Homegeneity Approach to High-Order Sliding Mode Design
,” Automatica
, 41
(5
), pp. 823
–830
.10.
Levant
, A.
, and Alelishvil
, L.
, 2007
, “Integral High-Order Sliding Modes
,” IEEE Trans. Autom. Control
, 52
(7
), pp. 1278
–1282
.11.
Dinuzzo
, F.
, and Ferrara
, A.
, 2010
, “Higher Order Sliding Mode Controllers With Optimal Reaching
,” IEEE Trans. Autom. Control
, 54
(9
), pp. 2126
–2136
.12.
Feng
, Y.
, Han
, F.
, and Yu
, X.
, 2014
, “Chattering Free Full-Order Sliding-Mode Control
,” Automatica
, 50
(4
), pp. 1310
–1314
.13.
Dadras
, S.
, and Momeni
, H. R.
, 2014
, “Fractional-Order Dynamic Output Feedback Sliding Mode Control Design for Robust Stabilization of Uncertain Fractional-Order Nonlinear Systems
,” Asian J. Control
, 16
(2
), pp. 1
–9
.14.
Ding
, S.
, Levant
, A.
, and Li
, S.
, 2016
, “Simple Homogeneous Sliding-Mode Controller
,” Automatica
, 67
, pp. 22
–32
.15.
Incremona
, G. P.
, Rubagotti
, M.
, and Ferrara
, A.
, 2017
, “Sliding Mode Control of Constrained Nonlinear System
,” IEEE Trans. Autom. Control
, 62
(6
), pp. 2965
–2972
.16.
Song
, J.
, Niu
, Y.
, and Zou
, Y.
, 2017
, “Finite-Time Stabilization via Sliding Mode Control
,” IEEE Trans. Autom. Control
, 62
(3
), pp. 1478
–1483
.17.
Oliveira
, T. R.
, Estrada
, A.
, and Fridman
, L. M.
, 2017
, “Global and Exact Differentiator With Dynamic Gains for Output-Feedback Sliding Mode Control
,” Automatica
, 81
, pp. 156
–163
.18.
Levant
, A.
, and Livne
, M.
, 2012
, “Exact Differentiation of Signals With Unbounded Higher Derivatives
,” IEEE Trans. Autom. Control
, 57
(4
), pp. 1076
–1080
.19.
Khalil
, H. K.
, 1992
, Nonlinear Systems
, Macmillan Publishing
, New York.20.
Hunter
, J. D.
, 2007
, “Matplotlib: A 2D Graphics Environment
,” Comput. Sci. Eng.
, 9
(3
), pp. 90
–95
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