Abstract

An active suspension system ensures the controllability of a vehicle in the vertical direction, which greatly enhances the control redundancy and safety of an intelligent driven vehicle. However, many calibrated model parameters are not conducive to the application of optimal control. To reduce the control cost of active suspension, a model-free H output feedback control method is studied in this research. First, the optimal governing equation of the active suspension is transformed into a zero-sum game problem of two players, and an off-policy reinforcement learning algorithm is established to solve the game algebraic Riccati equation. This method could overcome the disadvantage of constant interactions between Q-learning and the environment. Secondly, with the consideration that some state variables are difficult to measure, a data-driven H output feedback controller is designed using road sensing information and historical measurement data, and the Bellman equation of the system is solved using the least squares method to obtain the optimal control solution of the active suspension. The simulation and rapid prototype experimental results show that the proposed method could produce the optimal control strategy of the system without model parameters, overcome the strong dependence and sensitivity of traditional design methods to model parameters and improve the robust control effect of the active suspension.

References

1.
Yan
,
S.
,
Sun
,
W.
,
Yu
,
X.
, and
Gao
,
H.
,
2022
, “
Adaptive Sensor Fault Accommodation for Vehicle Active Suspensions Via Partial Measurement Information
,”
IEEE Trans. Cybern.
,
52
(
11
), pp.
12290
12301
.10.1109/TCYB.2021.3072219
2.
Ahmad
,
I.
,
Ge
,
X.
, and
Han
,
Q.
,
2021
, “
Decentralized Dynamic Event-Triggered Communication and Active Suspension Control of In-Wheel Motor Driven Electric Vehicles With Dynamic Damping
,”
IEEE/CAA J. Autom. Sin.
,
8
(
5
), pp.
971
986
.10.1109/JAS.2021.1003967
3.
Sun
,
W.
,
Zhao
,
Y.
,
Li
,
J.
,
Zhang
,
L.
, and
Gao
,
H.
,
2012
, “
Active Suspension Control With Frequency Band Constraints and Actuator Input Delay
,”
IEEE Trans. Ind. Electron.
,
59
(
1
), pp.
530
537
.10.1109/TIE.2011.2134057
4.
Na
,
J.
,
Huang
,
Y.
,
Pei
,
Q.
,
Wu
,
X.
,
Gao
,
G.
, and
Li
,
G.
,
2020
, “
Active Suspension Control of Full-Car Systems Without Function Approximation
,”
IEEE/ASME Trans. Mechatronics
,
25
(
2
), pp.
779
791
.10.1109/TMECH.2019.2962602
5.
Jing
,
H.
,
Wang
,
R.
,
Li
,
C.
, and
Bao
,
J.
,
2019
, “
Robust Finite-Frequency H Control of Full-Car Active Suspension
,”
J. Sound Vib.
,
441
, pp.
221
239
.10.1016/j.jsv.2018.06.047
6.
Rath
,
J. J.
,
Defoort
,
M.
,
Sentouh
,
C.
,
Karimi
,
H. R.
, and
Veluvolu
,
K. C.
,
2020
, “
Output-Constrained Robust Sliding Mode Based Nonlinear Active Suspension Control
,”
IEEE Trans. Ind. Electron.
,
67
(
12
), pp.
10652
10662
.10.1109/TIE.2020.2978693
7.
Pan
,
H.
,
Jing
,
X.
,
Sun
,
W.
, and
Gao
,
H.
,
2018
, “
A Bioinspired Dynamics-Based Adaptive Tracking Control for Nonlinear Suspension Systems
,”
IEEE Trans. Control Syst. Technol.
,
26
(
3
), pp.
903
914
.10.1109/TCST.2017.2699158
8.
Zheng
,
X.
,
Zhang
,
H.
,
Yan
,
H.
,
Yang
,
F.
,
Wang
,
Z.
, and
Vlacic
,
L.
,
2020
, “
Active Full-Vehicle Suspension Control Via Cloud-Aided Adaptive Backstepping Approach
,”
IEEE Trans. Cybern.
,
50
(
7
), pp.
3113
3124
.10.1109/TCYB.2019.2891960
9.
Na
,
J.
,
Huang
,
Y.
,
Wu
,
X.
,
Su
,
S. F.
, and
Li
,
G.
,
2020
, “
Adaptive Finite-Time Fuzzy Control of Nonlinear Active Suspension Systems With Input Delay
,”
IEEE Trans. Cybern.
,
50
(
6
), pp.
2639
2650
.10.1109/TCYB.2019.2894724
10.
Pan
,
H.
,
Zhang
,
D.
,
Sun
,
W.
, and
Yu
,
X.
,
2022
, “
Event-Triggered Adaptive Asymptotic Tracking Control of Uncertain MIMO Nonlinear Systems With Actuator Faults
,”
IEEE Trans. Cybern.
,
52
(
9
), pp.
8655
8667
.10.1109/TCYB.2021.3061888
11.
Pan
,
H.
,
Zhang
,
C.
, and
Sun
,
W.
,
2022
, “
Fault-Tolerant Multiplayer Tracking Control for Autonomous Vehicle Via Model-Free Adaptive Dynamic Programming
,”
IEEE Trans. Reliab.
, pp.
1
12
.10.1109/TR.2022.3208467
12.
Li
,
H.
,
Liu
,
H.
,
Gao
,
H.
, and
Shi
,
P.
,
2012
, “
Reliable Fuzzy Control for Active Suspension Systems With Actuator Delay and Fault
,”
IEEE Trans. Fuzzy Syst.
,
20
(
2
), pp.
342
357
.10.1109/TFUZZ.2011.2174244
13.
Zhang
,
M.
,
Jing
,
X.
, and
Wang
,
G.
,
2021
, “
Bioinspired Nonlinear Dynamics-Based Adaptive Neural Network Control for Vehicle Suspension Systems With Uncertain/Unknown Dynamics and Input Delay
,”
IEEE Trans. Ind. Electron.
,
68
(
12
), pp.
12646
12656
.10.1109/TIE.2020.3040667
14.
Wang
,
T.
, and
Li
,
Y.
,
2022
, “
Neural-Network Adaptive Output-Feedback Saturation Control for Uncertain Active Suspension Systems
,”
IEEE Trans. Cybern.
,
52
(
3
), pp.
1881
1890
.10.1109/TCYB.2020.3001581
15.
Jin
,
X.
,
Wang
,
J.
,
Yan
,
Z.
,
Xu
,
L.
,
Yin
,
G.
, and
Chen
,
N.
,
2022
, “
Robust Vibration Control for Active Suspension System of In-Wheel-Motor-Driven Electric Vehicle Via μ-Synthesis Methodology
,”
ASME J. Dyn. Syst., Meas., Control
,
144
(
5
), p.
051007
.10.1115/1.4053661
16.
Li
,
W.
,
Xie
,
Z.
,
Cao
,
Y.
,
Wong
,
P. K.
, and
Zhao
,
J.
,
2021
, “
Sampled-Data Asynchronous Fuzzy Output Feedback Control for Active Suspension Systems in Restricted Frequency Domain
,”
IEEE/CAA J. Autom. Sin.
,
8
(
5
), pp.
1052
1066
.10.1109/JAS.2020.1003306
17.
Zhang
,
J.
,
Sun
,
W.
, and
Jing
,
H.
,
2019
, “
Nonlinear Robust Control of Antilock Braking Systems Assisted by Active Suspensions for Automobile
,”
IEEE Trans. Control Syst. Technol.
,
27
(
3
), pp.
1352
1359
.10.1109/TCST.2018.2810823
18.
Pan
,
H.
, and
Sun
,
W.
,
2019
, “
Nonlinear Output Feedback Finite-Time Control for Vehicle Active Suspension Systems
,”
IEEE Trans. Ind. Inf.
,
15
(
4
), pp.
2073
2082
.10.1109/TII.2018.2866518
19.
Zhang
,
M.
, and
Jing
,
X.
,
2022
, “
Energy-Saving Robust Saturated Control for Active Suspension Systems Via Employing Beneficial Nonlinearity and Disturbance
,”
IEEE Trans. Cybern.
,
52
(
10
), pp.
10089
10100
.10.1109/TCYB.2021.3069632
20.
Dinh
,
H. T.
,
Trinh
,
T. D.
, and
Tran
,
V. N.
,
2021
, “
Saturated RISE Feedback Control for Uncertain Nonlinear Macpherson Active Suspension System to Improve Ride Comfort
,”
ASME J. Dyn. Syst., Meas., Control
,
143
(
1
), p.
011004
.10.1115/1.4048188
21.
Huang
,
Y.
,
Wu
,
J.
,
Na
,
J.
,
Han
,
S.
, and
Gao
,
G.
,
2022
, “
Unknown System Dynamics Estimator for Active Vehicle Suspension Control Systems With Time-Varying Delay
,”
IEEE Trans. Cybern.
,
52
(
8
), pp.
8504
8514
.10.1109/TCYB.2021.3063225
22.
Pang
,
H.
,
Wang
,
Y.
,
Zhang
,
X.
, and
Xu
,
Z.
,
2019
, “
Robust State-Feedback Control Design for Active Suspension System With Time-Varying Input Delay and Wheelbase Preview Information
,”
J. Franklin Inst.
,
356
(
4
), pp.
1899
1923
.10.1016/j.jfranklin.2019.01.011
23.
Ge
,
X.
,
Ahmad
,
I.
,
Han
,
Q. L.
,
Wang
,
J.
, and
Zhang
,
X. M.
,
2021
, “
Dynamic Event-Triggered Scheduling and Control for Vehicle Active Suspension Over Controller Area Network
,”
Mech. Syst. Signal Process.
,
152
, p.
107481
.10.1016/j.ymssp.2020.107481
24.
Xue
,
W.
,
Li
,
K.
,
Chen
,
Q.
, and
Liu
,
G.
,
2019
, “
Mixed FTS/H Control of Vehicle Active Suspensions With Shock Road Disturbance
,”
Veh. Syst. Dyn.
,
57
(
6
), pp.
841
854
.10.1080/00423114.2018.1490023
25.
Li
,
W.
,
Xie
,
Z.
,
Wong
,
P. K.
,
Ma
,
X.
,
Cao
,
Y.
, and
Zhao
,
J.
,
2019
, “
Nonfragile
H
Control of Delayed Active Suspension Systems in Finite Frequency Under Nonstationary Running
,”
ASME J. Dyn. Syst., Meas., Control
,
141
(
6
), p.
061001
.10.1115/1.4042468
26.
Liu
,
W.
,
Wang
,
R.
,
Ding
,
R.
,
Meng
,
X.
, and
Yang
,
L.
,
2020
, “
On-Line Estimation of Road Profile in Semi-Active Suspension Based on Unsprung Mass Acceleration
,”
Mech. Syst. Signal Process.
,
135
, p.
106370
.10.1016/j.ymssp.2019.106370
27.
Zhao
,
B.
,
Nagayama
,
T.
, and
Xue
,
K.
,
2019
, “
Road Profile Estimation, and Its Numerical and Experimental Validation, by Smartphone Measurement of the Dynamic Responses of an Ordinary Vehicle
,”
J. Sound Vib.
,
457
, pp.
92
117
.10.1016/j.jsv.2019.05.015
28.
Zhang
,
Q.
,
Hou
,
J.
,
Hu
,
X.
,
Yuan
,
L.
,
Jankowski
,
Ł.
,
An
,
X.
, and
Duan
,
Z.
,
2022
, “
Vehicle Parameter Identification and Road Roughness Estimation Using Vehicle Responses Measured in Field Tests
,”
Measurement
,
199
, p.
111348
.10.1016/j.measurement.2022.111348
29.
Li
,
P.
,
Lam
,
J.
, and
Cheung
,
K. C.
,
2014
, “
Velocity-Dependent Multi-Objective Control of Vehicle Suspension With Preview Measurements
,”
Mechatronics
,
24
(
5
), pp.
464
475
.10.1016/j.mechatronics.2014.04.008
30.
Wu
,
J.
,
Zhou
,
H.
,
Liu
,
Z.
, and
Gu
,
M.
,
2020
, “
Ride Comfort Optimization Via Speed Planning and Preview Semi-Active Suspension Control for Autonomous Vehicles on Uneven Roads
,”
IEEE Trans. Veh. Technol.
,
69
(
8
), pp.
8343
8355
.10.1109/TVT.2020.2996681
31.
Göhrle
,
C.
,
Schindler
,
A.
,
Wagner
,
A.
, and
Sawodny
,
O.
,
2015
, “
Road Profile Estimation and Preview Control for Low-Bandwidth Active Suspension Systems
,”
IEEE/ASME Trans. Mechatronics
,
20
(
5
), pp.
2299
2310
.10.1109/TMECH.2014.2375336
32.
Kiumarsi
,
B.
,
Lewis
,
F. L.
, and
Jiang
,
Z. P.
,
2017
, “H
Control of Linear Discrete-Time Systems: Off-Policy Reinforcement Learning
,”
Automatica
,
78
, pp.
144
152
.10.1016/j.automatica.2016.12.009
33.
Valadbeigi
,
A. P.
,
Sedigh
,
A. K.
, and
Lewis
,
F. L.
,
2020
, “H
Static Output-Feedback Control Design for Discrete-Time Systems Using Reinforcement Learning
,”
IEEE Trans. Neural Networks Learn. Syst.
,
31
(
2
), pp.
396
406
.10.1109/TNNLS.2019.2901889
34.
Kim
,
J. H.
, and
Lewis
,
F. L.
,
2010
, “
Model-Free
H
Control Design for Unknown Linear Discrete-Time Systems Via Q-Learning With LMI
,”
Automatica
,
46
(
8
), pp.
1320
1326
.10.1016/j.automatica.2010.05.002
35.
Li
,
S.
,
Durdevic
,
P.
, and
Yang
,
Z.
,
2021
, “
Model-Free
H
Tracking Control for de-Oiling Hydrocyclone Systems Via Off-Policy Reinforcement Learning
,”
Automatica
,
133
, p.
109862
.10.1016/j.automatica.2021.109862
36.
Luo
,
B.
,
Wu
,
H. N.
, and
Huang
,
T.
,
2015
, “
Off-Policy Reinforcement Learning for
H
Control Design
,”
IEEE Trans. Cybern.
,
45
(
1
), pp.
65
76
.10.1109/TCYB.2014.2319577
37.
Lewis
,
F. L.
,
Vrabie
,
D.
, and
Syrmos
,
V.
,
2012
,
Optimal Control
, 3rd ed.,
Wiley
,
Hoboken, NJ
.
38.
Lewis
,
F. L.
, and
Vamvoudakis
,
K. G.
,
2011
, “
Reinforcement Learning for Partially Observable Dynamic Processes: Adaptive Dynamic Programming Using Measured Output Data
,”
IEEE Trans. Syst., Man, Cybern., Part B (Cybern.)
,
41
(
1
), pp.
14
25
.10.1109/TSMCB.2010.2043839
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