IEEE Systems, Man and Cybernetics Magazine - October 2023 - 43

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State Error Brought by Delay
State Error Brought by Prediction
Figure 27. The evolution of the state error brought
by the delay and prediction (corresponding to
Figure 23). (a) Intervehicle distance error subject
to expected distance. (b) Intervehicle speed error.
(c) Acceleration of the following vehicle.
performance under specific delays. However, from another
perspective, the predictor-observer structure will distinctly
improve the control performance under delays
under the same controller gain.
Remark 10
It can be noticed that the delay considered in the simulation
is far longer than the regular network-induced delay.
Thus, it needs to be clarified again that the sensing delay
considered in the simulation contains the sensing information
processing time, which might also be time-consuming.
That is also why the delay length setting in this study
is higher than the regular network-induced end-to-end
delay. Besides, the simulation considers some worst cases
that might occur when network congestion happens.
Conclusion
In this article, we investigated the control strategy for the
connected vehicle cloud control system with bounded sensing
delay. The predictor-observer structure-based controller
has been adopted and designed to compensate for the
delay, considering both known and unknown delay cases.
With system augmentation, the closed-loop system with the
predictor-observer pattern controller has been modeled as
an equivalent interconnected system, and its stability has
been analyzed. A sufficient condition guaranteeing stability
80 100 120
80 100 120
has been derived based on the SBRL and LKF methods. A
CCL-based iterative algorithm has also been provided to
determine feasible controller and observer gains. In simulation,
the proposed control and delay compensation strategies
have been verified under connected vehicle lateral and
longitudinal control scenarios. Simulation results have
shown that the proposed prediction strategies could estimate
system states, and the control strategies could perfectly
stabilize the system under both known and unknown
delay cases. The simulation results also reveal that if the
delay is known to the controller, a more accurate estimation
of the system states could be conducted with the synchronized
predictor-observer method, at the cost of measuring
output delay in real time and extra memory on the past control
input. The methodology used in this study could also
be the foundation for analyzing delay compensation systems
considering both input and output delays, which will
be a topic in our future research and publications. In general,
although the predictor-observer structured controller
was not initially proposed by this study, the self-contained
proof of the stability of the method considering bounded
model uncertainty and bounded delay has been provided in
the discrete space. More important, to the authors' knowledge,
only a few related studies evaluate and compare two
different predictor-observer control methods under the
simulation platform with a higher confidence level [37],
which narrows the gap toward deploying the delay compensation
method in real vehicle control systems.
Finally, it should be admitted that the stabilization analysis
in this study exposes the conservatism problem. In
other words, the proposed method may not be able to find
feasible solutions in cases with some extreme delay. At the
same time, the experiments have indicated that some infeasible
controller gain could also stabilize the system. Therefore,
how to describe the delayed term mathematically with
less conservatism also poses a topic for future studies.
Acknowledgment
This work was supported by the National Natural Science
Foundation of China (Grant 52072212), Tsinghua University-
Didi Joint Research Center for Future Mobility, and Joint
Laboratory for Internet of Vehicle, Ministry of Education-
China Mobile Communications. This article has supplementary
downloadable material available at http://doi.org/
10.1109/MSMC.2023.3277697, provided by the authors.
About the Authors
Jian Pan (pja17@mails.tsinghua.edu.cn) is with the
School of Vehicle and Mobility, Tsinghua University, Beijing
100084, China.
Qing Xu (qingxu@tsinghua.edu.cn) is with the School
of Vehicle and Mobility, Tsinghua University, Beijing
100084, China.
Keqiang Li (likq@tsinghua.edu.cn) is with the School
of Vehicle and Mobility, Tsinghua University, Beijing
100084, China.
October 2023 IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE 43
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http://www.doi.org/10.11097msmc.2023.3277697 http://www.doi.org/10.11097msmc.2023.3277697
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