Abstract
This paper presents a novel discrete-time sliding mode control (DSMC) for a general class of discrete-time chaotic systems with input nonlinearity and uncertainties. Unlike the conventional sliding mode control (SMC), the sliding surface is constructed by applying the eigenvalue assignment method to the overall system in discrete-time domain, not to the reduced system on the sliding mode in continue-time domain. The design of sliding surface and the existence of quasi-sliding mode are two significant issues, which have been addressed. The stability of the overall closed-loop system is guaranteed. In addition, the undesirable chattering phenomenon and the reaching phase are eliminated. Simulation results demonstrate the feasibility and effectiveness of the proposed scheme.
Issue Section:
Research Papers
References
1.
Vaidyanathan
,
S.
, and
Sampath
,
S.
, 2011
, “
Global Chaos Synchronization of Hyperchaotic Lorenz Systems by Sliding Mode Control
,” Adv. Digital Image Process. Inf. Technol. Commun. Comput. Inf. Sci.
,
205
, pp. 156
–164
.10.1007/978-3-642-24055-3_162.
Ott
,
E.
,
Grebogi
,
C.
, and
Yorke
,
J. A.
, 1990
, “
Controlling Chaos
,” Phys. Rev. Lett.
,
64
(11
), pp. 1196
–1199
.10.1103/PhysRevLett.64.11963.
Pecora
,
L. M.
, and
Carroll
,
T. L.
, 1990
, “
Synchronization in Chaotic Systems
,” Phys. Rev. Lett.
,
64
(8
), pp. 821
–824
.10.1103/PhysRevLett.64.8214.
Nazzal
,
J. M.
, and
Natsheh
,
A. N.
, 2007
, “
Chaos Control Using Sliding Mode Theory
,” Chaos, Solitons Fractals
,
33
(2
), pp. 695
–702
.10.1016/j.chaos.2006.01.0715.
Yan
,
J. J.
,
Yang
,
Y. S.
,
Chiang
,
T. Y.
, and
Chen
,
C. Y.
, 2007
, “
Robust Synchronization of Unified Chaotic Systems Via Sliding Mode Control
,” Chaos, Solitons Fractals
,
34
(3
), pp. 947
–954
.10.1016/j.chaos.2006.04.0036.
Aghababa
,
M. P.
, and
Akbari
,
M. E.
, 2012
, “
A Chattering-Free Robust Adaptive Sliding Mode Controller for Synchronization of Two Different Chaotic Systems With Unknown Uncertainties and External Disturbances
,” Appl. Math. Comput.
,
218
(9
), pp. 5757
–5768
.10.1016/j.amc.2011.11.0807.
Pai
,
M. C.
, 2012
, “
Adaptive Sliding Mode Observer-Based Synchronization for Uncertain Chaotic Systems
,” Asian J. Control
,
14
(3
), pp. 736
–743
.10.1002/asjc.2908.
Mobayen
,
S.
,
Baleanu
,
D.
, and
Tchier
,
F.
, 2017
, “
Second-Order Fast Terminal Sliding Mode Control Design Based on LMI for a Class of Non-Linear Uncertain Systems and Its Application to Chaotic Systems
,” J. Vib. Control
,
23
(18
), pp. 2912
–2925
.10.1177/10775463156238879.
Dadras
,
S.
,
Dadras
,
S.
, and
Momeni
,
H.
, 2017
, “
Linear Matrix Inequality Based Fractional Integral Sliding-Mode Control of Uncertain Fractional-Order Nonlinear Systems
,” ASME J. Dyn. Syst., Meas., Control
,
139
(11
), p. 111003
.10.1115/1.403680710.
Mobayen
,
S.
, 2018
, “
Chaos Synchronization of Uncertain Chaotic Systems Using Composite Nonlinear Feedback Based Integral Sliding Mode Control
,” ISA Trans.
,
77
, pp. 100
–111
.10.1016/j.isatra.2018.03.02611.
Mohammadpour
,
S.
, and
Binazadeh
,
T.
, 2018
, “
Robust Finite-Time Synchronization of Uncertain Chaotic Systems: Application on Duffing-Holmes System and Chaos Gyros
,” Syst. Sci. Control Eng.
,
6
(1
), pp. 28
–36
.10.1080/21642583.2018.142869512.
Mofid
,
O.
,
Mobayen
,
S.
, and
Khooban
,
M. H.
, 2018
, “
Sliding Mode Disturbance Observer Control Based on Adaptive Synchronization in a Class of Fractional‐Order Chaotic Systems
,” Int. J. Adapt. Control Signal Process.
,
33
(3
), pp. 462
–474
.10.1002/acs.296513.
Song
,
C.
,
Fei
,
S.
,
Cao
,
J.
, and
Huang
,
C.
, 2019
, “
Robust Synchronization of Fractional-Order Uncertain Chaotic Systems Based on Output Feedback Sliding Mode Control
,” Mathematics
,
7
(7
), p. 599
.10.3390/math707059914.
Yang
,
C. C.
, and
Lin
,
C. L.
, 2015
, “
Adaptive Sliding Mode Control for Chaotic Synchronization of Oscillator With Input Nonlinearity
,” J. Vib. Control
,
21
(3
), pp. 601
–610
.10.1177/107754631348724315.
Pai
,
M. C.
, 2016
, “
Quasi-Output Feedback Global Sliding Mode Tracker for Uncertain Systems With Input Nonlinearity
,” Nonlinear Dyn.
,
86
(2
), pp. 1215
–1225
.10.1007/s11071-016-2958-z16.
Afshari
,
M.
,
Mobayen
,
S.
,
Hajmohammadi
,
R.
, and
Baleanu
,
D.
, 2018
, “
Global Sliding Mode Control Via Linear Matrix Inequality Approach for Uncertain Chaotic Systems With Input Nonlinearities and Multiple Delays
,” ASME J. Comput. Nonlinear Dyn.
,
13
(3
), p. 031008
.10.1115/1.403864117.
Mohammadpour
,
S.
, and
Binazadeh
,
T.
, 2018
, “
Observer-Based Synchronization of Uncertain Chaotic Systems Subject to Input Saturation
,” Trans. Inst. Meas. Control
,
40
(8
), pp. 2526
–2535
.10.1177/014233121770543518.
Mystkowski
,
A.
, 2019
, “
Lyapunov Sliding-Mode Observers With Application for Active Magnetic Bearing Operated With Zero-Bias Flux
,” ASME J. Dyn. Sys. Meas. Control
,
141
(4
), p. 041006
.10.1115/1.404197819.
Pai
,
M. C.
, 2019
, “
Synchronization of Unified Chaotic Systems Via Adaptive Nonsingular Fast Terminal Sliding Mode Control
,” Int. J. Dyn. Control
,
7
(3
), pp. 1101
–1109
.10.1007/s40435-018-0486-z20.
Cruz-Zavala
,
E.
,
Moreno
,
J. A.
, and
Fridman
,
L.
, 2013
, “
Fast Second-Order Sliding Mode Control Design Based on Lyapunov Function
,” IEEE Conference on Decision and Control
, Florence, Italy, Dec. 10–13, pp. 2858
–2863
.10.1109/CDC.2013.676031721.
Kochalummoottil
,
J.
,
Shtessel
,
Y. B.
,
Moreno
,
J. A.
, and
Fridman
,
L.
, 2011
, “
Adaptive Twist Sliding Mode Control: A Lyapunov Design
,” IEEE Conference on Decision and Control and European Control Conference
, Orlando, FL, Dec. 10–15, pp. 7623
–7628
.10.1109/CDC.2011.616098222.
Yan
,
B.
,
Dai
,
P.
,
Liu
,
R.
,
Xing
,
M.
, and
Liu
,
S.
, 2019
, “
Adaptive Super-Twisting Sliding Mode Control of Variable Sweep Morphing Aircraft
,” Aerosp. Sci. Technol.
,
92
, pp. 198
–210
.10.1016/j.ast.2019.05.06323.
Pai
,
M.
, 2020
, “
Adaptive Super-Twisting Terminal Sliding Mode Control for Nonlinear Systems With Multiple Inputs
,” Int. J. Dyn. Control
,
8
(2
), pp. 666
–674
.10.1007/s40435-019-00593-y24.
Majidabad
,
S. S.
, and
Shandiz
,
H. T.
, 2013
, “
Discrete-Time Terminal Sliding Mode Control of Chaotic Lorenz System
,” J. Control Syst. Eng.
,
1
(1
), pp. 1
–8
.10.18005/JCSE010100125.
Pai
,
M. C.
, 2014
, “
Global Synchronization of Uncertain Chaotic Systems Via Discrete-Time Sliding Mode Control
,” Appl. Math. Comput.
,
227
, pp. 663
–671
.10.1016/j.amc.2013.11.07526.
Yan
,
J.-J.
,
Chen
,
C.-Y.
, and
Tsai
,
S.-H.
, 2016
, “
Hybrid Chaos Control of Continuous Unified Chaotic Systems Using Discrete Rippling Sliding Mode Control
,” Nonlinear Anal. Hybrid Syst.
,
22
, pp. 276
–283
.10.1016/j.nahs.2016.05.00427.
Hu
,
F.
, 2017
, “
Sliding Mode Control of Discrete Chaotic System Based on Multimodal Function Series Coupling
,” Math. Probl. Eng.
,
2017
, pp. 1
–11
.10.1155/2017/842341328.
Draženović
,
B.
, 1969
, “
The Invariance Conditions in Variable Structure Systems
,” Automatica
,
5
(3
), pp. 287
–295
.10.1016/0005-1098(69)90071-529.
Utkin
,
V. I.
, 1977
, “
Sliding Mode Systems With Sliding Modes
,” IEEE Trans. Autom. Control
,
22
(2
), pp. 212
–222
.10.1109/TAC.1977.110144630.
Mobayen
,
S.
, and
Tchier
,
F.
, 2017
, “
Design of an Adaptive Chattering Avoidance Global Sliding Mode Tracker for Uncertain Non-Linear Time-Varying Systems
,” Trans. Inst. Meas. Control
,
39
(10
), pp. 1547
–1558
.10.1177/014233121664404631.
Spurgeon
,
S. K.
, 1992
, “
Hyperplane Design Techniques for Discrete-Time Variable Structure Control Systems
,” Int. J. Control
,
55
(2
), pp. 445
–456
.10.1080/0020717920893424832.
Chang
,
J. L.
, 2008
, “
Discrete Sliding-Mode Control of MIMO Linear Systems
,” Asian J. Control
,
4
(2
), pp. 217
–222
.10.1111/j.1934-6093.2002.tb00348.x33.
Utkin
,
V. I.
, 1993
, Sliding Modes in Control Optimization
,
Springer-Verlag
,
New York
.34.
Yu
,
H. C.
, and
Liu
,
T. S.
, 2008
, “
Sliding Mode Control Using Virtual Eigenvalue Method for Compact Optical Image Stabilization Actuators
,” IEEE Trans. Magn.
,
44
(11
), pp. 4074
–4077
.10.1109/TMAG.2008.200278735.
Hsiao
,
W. Y.
, and
Chiang
,
H. H.
, 2012
, “
Sliding-Mode-Control With Filtered State- Feedback or Disturbance Attenuation of Active Suspension Systems
,” Int. J. Eng. Ind.
,
3
(1
), pp. 67
–78
.10.4156/ijei.vol3.issue1.736.
Sarpturk
,
S. Z.
,
Istefanopulos
,
Y.
, and
Kaynak
,
O.
, 1987
, “
On the Stability of Discrete-Time Sliding Mode Control Systems
,” IEEE Trans. Autom. Control
,
32
(10
), pp. 930
–937
.10.1109/TAC.1987.1104468Copyright © 2020 by ASME
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