Abstract

The model uncertainty of the steer-by-wire (SbW) system and the limitation of communication bandwidth will have a negative effect on its control performance. For this reason, this paper proposes an event-triggered high-order sliding mode control for uncertain SbW systems. First, to save communication and computing resources, an event-triggering mechanism that depends on the system state is proposed for the SbW system, such that both communication and computing resources can be saved. Second, an event-triggered adaptive higher-order sliding mode (ET-AHOSM) control is proposed for the closed-loop SbW system. The assumptions about the global Lipschitz of nonlinearity and the a priori bounds of the disturbance are no longer required in the control design. Much importantly, the control input continuity can be guaranteed even there is the event-triggering communication in the controller-to-actuator channel. Theoretical analysis shows that the global practical finite-time stability of the closed-loop SbW system can be obtained while avoiding Zeno behavior of the event-triggered control system. Finally, numerical simulation and experiments show that the designed control method can reduce more than 1/2 of the calculation and communication resources while ensuring satisfactory tracking accuracy.

References

1.
Baviskar
,
A.
,
Wagner
,
J. R.
,
Dawson
,
D. M.
,
Braganza
,
D.
, and
Setlur
,
P.
,
2009
, “
An Adjustable Steer-by-Wire Haptic-Interface Tracking Controller for Ground Vehicles
,”
IEEE Trans. Veh. Technol.
,
58
(
2
), pp.
546
554
.10.1109/TVT.2008.925317
2.
Yih
,
P.
, and
Gerdes
,
J.
,
2005
, “
Modification of Vehicle Handling Characteristics Via Steer-by-Wire
,”
IEEE Trans. Contr. Syst. Technol.
,
13
(
6
), pp.
965
976
.10.1109/TCST.2005.854320
3.
Kirli
,
A.
,
Chen
,
Y.
,
Okwudire
,
C.
, and
Ulsoy
,
G.
,
2019
, “
Torque-Vectoring-Based Backup Steering Strategy for Steer-by-Wire Autonomous Vehicles With Vehicle Stability Control
,”
IEEE Trans. Veh. Technol.
,
68
(
8
), pp.
7319
7328
.10.1109/TVT.2019.2921016
4.
Wu
,
X. D.
,
Zhang
,
M. M.
, and
Xu
,
M.
,
2019
, “
Active Tracking Control for Steer-by-Wire System With Disturbance Observer
,”
IEEE Trans. Veh. Technol.
,
68
(
6
), pp.
5483
5493
.10.1109/TVT.2019.2910540
5.
Norouzi
,
A.
,
Kazemi
,
R.
, and
Azadi
,
S.
,
2018
, “
Vehicle Lateral Control in the Presence of Uncertainty for Lane Change Maneuver Using Adaptive Sliding Mode Control With Fuzzy Boundary Layer
,”
Proc. I. Mech. E., Part I: J. Syst. Contr. Eng.
,
232
(
1
), pp.
12
28
.10.1177/0959651817733222
6.
Ji
,
X.
,
Yang
,
K.
,
Na
,
X.
,
Lv
,
C.
,
Liu
,
Y.
, and
Liu
,
Y.
,
2019
, “
Feedback Game-Based Shared Control Scheme Design for Emergency Collision Avoidance: A Fuzzy-Lqr Approach
,”
ASME J. Dyn. Sys., Meas., Contr.
,
141
(
8
), p.
081005
.10.1115/1.4042880
7.
Wang
,
H.
,
Kong
,
H.
,
Man
,
Z.
,
Tuan
,
D. M.
,
Cao
,
Z.
, and
Shen
,
W.
,
2014
, “
Sliding Mode Control for Steer-by-Wire Systems With ac Motors in Road Vehicles
,”
IEEE Trans. Ind. Electron.
,
61
(
3
), pp.
1596
1611
.10.1109/TIE.2013.2258296
8.
Sun
,
Z.
,
Zheng
,
J.
,
Man
,
Z.
, and
Wang
,
H.
,
2016
, “
Robust Control of a Vehicle Steer-by-Wire System Using Adaptive Sliding Mode
,”
IEEE Trans. Ind. Electron.
,
63
(
4
), pp.
2251
2262
.10.1109/TIE.2015.2499246
9.
Sun
,
Z.
,
Zheng
,
J.
,
Man
,
Z.
, and
Wang
,
H.
,
2017
, “
Adaptive Fast Non-Singular Terminal Sliding Mode Control for a Vehicle Steer-by-Wire System
,”
IET Contr. Theory Appl.
,
11
(
8
), pp.
1245
1254
.10.1049/iet-cta.2016.0205
10.
Wang
,
H.
,
Man
,
Z.
,
Kong
,
H.
,
Zhao
,
Y.
,
Yu
,
M.
,
Cao
,
Z.
,
Zheng
,
J.
, and
Do
,
M.
,
2016
, “
Design and Implementation of Adaptive Terminal Sliding Mode Control on a Steer-by-Wire Equipped Road Vehicle
,”
IEEE Trans. Ind. Electron.
,
63
(
9
), pp.
5774
5785
.10.1109/TIE.2016.2573239
11.
Lin
,
F.
,
Hung
,
Y.
, and
Ruan
,
K.
,
2014
, “
An Intelligent Second-Order Sliding-Mode Control for an Electric Power Steering System Using a Wavelet Fuzzy Neural Network
,”
IEEE Trans. Fuzzy Syst.
,
22
(
6
), pp.
1598
1611
.10.1109/TFUZZ.2014.2300168
12.
Tabuada
,
P.
,
2007
, “
Event-Triggered Real-Time Scheduling of Stabilizing Control Tasks
,”
IEEE Trans. Automat. Contr.
,
52
(
9
), pp.
1680
1685
.10.1109/TAC.2007.904277
13.
Henningsson
,
T.
,
Johannesson
,
E.
, and
Cervin
,
A.
,
2008
, “
Sporadic Event-Based Control of First-Order Linear Stochastic Systems
,”
Automatica
,
44
(
11
), pp.
2890
2895
.10.1016/j.automatica.2008.03.026
14.
Li
,
H.
, and
Shi
,
Y.
,
2014
, “
Event-Triggered Robust Model Predictive Control of Continuous-Time Nonlinear Systems
,”
Automatica
,
50
(
5
), pp.
1507
1513
.10.1016/j.automatica.2014.03.015
15.
Liu
,
T. F.
, and
Jiang
,
Z. P.
,
2015
, “
A Small-Gain Approach to Robust Event-Triggered Control of Nonlinear Systems
,”
IEEE Trans. Automat. Contr.
,
60
(
8
), pp.
2072
2085
.10.1109/TAC.2015.2396645
16.
Behera
,
A. K.
, and
Bandyopadhyay
,
B.
,
2016
, “
New Methodologies for Adaptive Sliding Mode Control
,”
Int. J. Contr.
,
89
(
9
), pp.
1916
1931
.10.1080/00207179.2016.1142617
17.
Zheng
,
G. W.
,
Xu
,
Y.
,
Lu
,
R.
,
Wu
,
Y.
, and
Huang
,
T.
,
2018
, “
Adaptive Neural Fault-Tolerant Control of a 3-Dof Model Helicopter System
,”
IEEE Trans. Syst., Man, Cybern., Syst.
,
46
(
2
), pp.
260
270
.10.1109/TSMC.2015.2426140
18.
Li
,
Z. C.
,
Hu
,
B.
,
Li
,
M.
, and
Luo
,
G. N.
,
2019
, “
String Stability Analysis for Vehicle Platooning Under Unreliable Communication Links With Event-Triggered Strategy
,”
IEEE Trans. Veh. Technol.
,
68
(
3
), pp.
2152
2164
.10.1109/TVT.2019.2891681
19.
Zhao
,
H.
,
Dai
,
X. W.
,
Zhang
,
Q.
, and
Ding
,
J. L.
,
2020
, “
Robust Event-Triggered Model Predictive Control for Multiple High-Speed Trains With Switching Topologies
,”
IEEE Trans. Veh. Technol.
,
69
(
5
), pp.
4700
4710
.10.1109/TVT.2020.2974979
20.
Li
,
H.
,
Yan
,
W.
, and
Shi
,
Y.
,
2018
, “
Triggering and Control Codesign in Self-Triggered Model Predictive Control of Constrained Systems: With Guaranteed Performance
,”
IEEE Trans. Automat. Contr.
,
63
(
11
), pp.
4008
4015
.10.1109/TAC.2018.2810514
21.
Fan
,
X. F.
, and
Wang
,
Z. S.
,
2020
, “
Event-Triggered Sliding Mode Control for a Class of t-s Fuzzy Systems
,”
IEEE Trans. Fuzzy Syst.
,
28
(
10
), pp.
2656
2664
.10.1109/TFUZZ.2019.2940867
22.
Jiang
,
B. P.
,
Karimi
,
H. R.
,
Kao
,
Y. G.
, and
Gao
,
C. C.
,
2020
, “
Takagi–Sugeno Model Based Event-Triggered Fuzzy Sliding-Mode Control of Networked Control Systems With Semi-Markovian Switchings
,”
IEEE Trans. Fuzzy Syst
,
28
(
4
), pp.
673
683
.10.1109/TFUZZ.2019.2914005
23.
Wu
,
L.
,
Gao
,
Y.
,
Liu
,
J.
, and
Li
,
H.
,
2017
, “
Event-Triggered Sliding Mode Control of Stochastic Systems Via Output Feedback
,”
Automatica
,
82
, pp.
79
92
.10.1016/j.automatica.2017.04.032
24.
Liu
,
Y.
,
Jiang
,
B. X.
,
Lu
,
J. Q.
,
Cao
,
J. D.
, and
Lu
,
G. P.
,
2020
, “
Event-Triggered Sliding Mode Control for Attitude Stabilization of a Rigid Spacecraft
,”
IEEE Trans. Syst., Man, Cybern., Syst.
,
50
(
9
), pp.
3290
3299
.10.1109/TSMC.2018.2867061
25.
Nair
,
R. R.
,
Behera
,
L.
, and
Kumar
,
S.
,
2019
, “
Multirobot Systems With Disturbances
,”
IEEE Trans. Contr. Syst. Technol.
,
27
(
1
), pp.
39
47
.10.1109/TCST.2017.2757448
26.
Li
,
M.
,
Shi
,
P.
,
Liu
,
M.
,
Zhang
,
Y. C.
, and
Wang
,
S. Y.
,
2020
, “
Event-Triggered-Based Adaptive Sliding Mode Control for T-S Fuzzy Systems With Actuator Failures and Signal Quantization
,”
IEEE Trans. Fuzzy Syst.
, epub.10.1109/TFUZZ.2020.2974175
27.
Kumari
,
B.
,
Behera
,
A. K.
, and
Bandyopadhyay
,
B.
,
2018
, “
Event-Triggered Sliding Mode-Based Tracking Control for Uncertain Euler–Lagrange Systems
,”
IET Contr. Theory Appl.
,
12
(
9
), pp.
1228
1235
.10.1049/iet-cta.2017.1114
28.
Levant
,
A.
,
1993
, “
Sliding Order and Sliding Accuracy in Sliding Mode Control
,”
Int. J. Contr.
,
58
(
6
), pp.
1247
1263
.10.1080/00207179308923053
29.
Laghrouche
,
S.
,
Plestan
,
F.
, and
Glumineau
,
A.
,
2007
, “
Higher Order Sliding Mode Control Based on Integral Sliding Mode
,”
Automatica
,
43
(
3
), pp.
531
537
.10.1016/j.automatica.2006.09.017
30.
Edwards
,
C.
, and
Shtessel
,
Y.
,
2016
, “
Adaptive Continuous Higher Order Sliding Mode Control
,”
Automatica
,
65
(
1
), pp.
183
190
.10.1016/j.automatica.2015.11.038
31.
Burton
,
J. A.
, and
Zinober
,
A. S. I.
,
1986
, “
Continuous Approximation of Variable Structure Control
,”
Int. J. Syst. Sci.
,
17
(
6
), pp.
875
885
.10.1080/00207728608926853
32.
Huang
,
Y. J.
,
Kuo
,
T. C.
, and
Chang
,
S. H.
,
2008
, “
Adaptive Sliding-Mode Control for Nonlinear Systems With Uncertain Parameters
,”
IEEE Trans. Syst. Man Cybern. B
,
38
(
2
), pp.
534
539
.10.1109/TSMCB.2007.910740
33.
Jiao
,
X. H.
,
Zhang
,
J. Y.
, and
Shen
,
T. L.
,
2014
, “
An Adaptive Servo Control Strategy for Automotive Electronic Throttle and Experimental Validation
,”
IEEE Trans. Ind. Electron
,
61
(
11
), pp.
6275
6284
.10.1109/TIE.2014.2311398
34.
Lu
,
K. F.
,
Xia
,
Y. Q.
,
Yu
,
C. M.
, and
Liu
,
H. L.
,
2016
, “
Finite-Time Tracking Control of Rigid Spacecraft Under Actuator Saturations and Faults
,”
IEEE Trans. Autom. Sci. Eng.
,
13
(
1
), pp.
368
381
.10.1109/TASE.2014.2379615
35.
Li
,
P.
,
Yu
,
X.
, and
Xiao
,
B.
,
2018
, “
Adaptive Quasi-Optimal Higher Order Sliding-Mode Control Without Gain Overestimation
,”
IEEE Trans. Ind. Informat.
,
14
(
9
), pp.
3881
3891
.10.1109/TII.2017.2787701
36.
Rosales
,
A.
,
Shtessel
,
Y.
,
Fridman
,
L.
, and
Panathula
,
C. B.
,
2017
, “
Chattering Analysis of Hosm Controlled Systems: Frequency Domain Approach
,”
IEEE Trans. Automat. Contr.
,
62
(
8
), pp.
4109
4115
.10.1109/TAC.2016.2619559
37.
Bartoszewicz
,
A.
, and
Latosinski
,
P.
,
2018
, “
Generalization of Gaos̈ Reaching Law for Higher Relative Degree Sliding Variables
,”
IEEE Trans. Automat. Contr.
,
63
(
9
), pp.
3173
3179
.10.1109/TAC.2018.2797193
38.
Panathula
,
C. B.
,
Rosales
,
A.
,
Shtessel
,
Y. B.
, and
Fridman
,
L. M.
,
2018
, “
Closing Gaps for Aircraft Attitude Higher Order Sliding Mode Control Certification Via Practical Stability Margins Identification
,”
IEEE Trans. Contr. Syst. Technol.
,
26
(
6
), pp.
2020
2034
.10.1109/TCST.2017.2753162
39.
Adaldo
,
A.
,
Alderisio
,
F.
,
Liuzza
,
D.
,
Shi
,
G.
,
Dimarogonas
,
D. V.
,
di Bernardo
,
M.
, and
Johansson
,
K. H.
,
2015
, “
Event-Triggered Pinning Control of Switching Networks
,”
IEEE Trans. Contr. Netw. Syst.
,
2
(
2
), pp.
204
213
.10.1109/TCNS.2015.2428531
40.
Li
,
Y. X.
, and
Yang
,
G. H.
,
2018
, “
Model-Based Adaptive Event-Triggered Control of Strict-Feedback Nonlinear Systems
,”
IEEE Trans. Neural Netw. Learn. Syst.
,
29
(
4
), pp.
1033
1045
.10.1109/TNNLS.2017.2650238
41.
Johansson
,
K. H.
,
Egersted
,
M.
,
Lygeros
,
J.
, and
Sastry
,
S.
,
1999
, “
On the Regularization of Zeno Hybrid Automata
,”
Syst. Contr. Lett.
,
38
(
3
), pp.
141
150
.10.1016/S0167-6911(99)00059-6
42.
Levant
,
A.
,
2005
, “
Homogeneity Approach to High-Order Sliding Mode Design
,”
Automatica
,
41
(
5
), pp.
823
830
.10.1016/j.automatica.2004.11.029
43.
Utkin
,
V. I.
, and
Poznyak
,
A. S.
,
2013
, “
Adaptive Sliding Mode Control With Application to Super-Twist Algorithm: Equivalent Control Method
,”
Automatica
,
49
(
1
), pp.
39
47
.10.1016/j.automatica.2012.09.008
44.
Yan
,
X. M.
,
Franck
,
P.
, and
Muriel
,
P.
,
2017
, “
A New Third-Order Sliding-Mode Controller Application to an Electropneumatic Actuator
,”
IEEE Trans. Contr. Syst. Technol.
,
25
(
2
), pp.
744
751
.10.1109/TCST.2016.2571664
45.
Tenoch
,
G. A. M. J.
, and
Leonid
,
F.
,
2012
, “
Variable Gain Super-Twisting Sliding Mode Control
,”
IEEE Trans. Automat. Contr.
,
57
(
8
), pp.
2100
2105
.10.1109/TAC.2011.2179878
46.
Li
,
J. P.
,
Yang
,
Y. N.
,
Hua
,
C. C.
, and
Guan
,
X. P.
,
2017
, “
Fixed-Time Backstepping Control Design for High-Order Strict-Feedback Non-Linear Systems Via Terminal Sliding Mode
,”
IET Contr. Theory Appl.
,
11
(
8
), pp.
1184
1193
.10.1049/iet-cta.2016.1143
47.
Huang
,
Y. X.
, and
Liu
,
Y. G.
,
2019
, “
Practical Tracking Via Adaptive Event-Triggered Feedback for Uncertain Nonlinear Systems
,”
IEEE Trans. Automat. Contr.
,
64
(
9
), pp.
3920
3927
.10.1109/TAC.2019.2891411
48.
Xin
,
L. Y.
, and
Hong
,
Y. G.
,
2018
, “
Observer-Based Fuzzy Adaptive Event-Triggered Control Codesign for a Class of Uncertain Nonlinear Systems
,”
IEEE Trans. Fuzzy Syst
,
26
(
3
), pp.
1589
1599
.10.1109/TFUZZ.2017.2735944
49.
Levant
,
A.
,
2003
, “
Higher-Order Sliding Modes, Differentiation and Output-Feedback Control
,”
Int. J. Contr.
,
76
(
9–10
), pp.
924
941
.10.1080/0020717031000099029
50.
Xing
,
L. T.
,
Wen
,
C. Y.
,
Liu
,
Z. T.
,
Su
,
H. Y.
, and
Cai
,
J. P.
,
2017
, “
Event-Triggered Adaptive Control for a Class of Uncertain Nonlinear Systems
,”
IEEE Trans. Automat. Contr.
,
62
(
4
), pp.
2071
2076
.10.1109/TAC.2016.2594204
51.
Xing
,
L. T.
,
Wen
,
C. Y.
,
Liu
,
Z. T.
,
Su
,
H. Y.
, and
Cai
,
J. P.
,
2019
, “
Event-Triggered Output Feedback Control for a Class of Uncertain Nonlinear Systems
,”
IEEE Trans. Automat. Contr.
,
64
(
1
), pp.
290
297
.10.1109/TAC.2018.2823386
52.
Li
,
Z.
,
Ring
,
P.
,
Macrae
,
K.
, and
Hinsch
,
A.
,
1991
,
Applied Nonlinear Control
,
Prentice Hall
, Upper Saddle River,
NJ.
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