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Abstract:
In contrast to the fruitful results in saturated control of ordinary differential equation (ODE) systems, there are few related studies for hyperbolic partial differential equation (PDE) systems. This paper focuses on the saturated boundary feedback stabilization problem for the Lighthill-Whitham-Richards (LWR) traffic flow model, in which a variable speed limit (VSL) device is applied at the downstream boundary in the presence of actuator saturation and a saturated boundary feedback controller is proposed to drive the traffic density to the steady state. By employing the Lyapunov function method along with a modified local sector condition, sufficient conditions for ensuring the local exponential stability of the LWR traffic flow system are developed in C1-norm. Remarkably, the proposed sufficient conditions establish a relationship between the control gain and the region of exponential stability (RES), and thus the maximal RES can be determined by introducing an optimization criterion. Lastly, numerical simulations are performed to verify the effectiveness of the theoretical results.(c) 2023 Elsevier B.V. All rights reserved.
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Source :
SYSTEMS & CONTROL LETTERS
ISSN: 0167-6911
Year: 2023
Volume: 173
2 . 6 0 0
JCR@2022
ESI Discipline: ENGINEERING;
ESI HC Threshold:19
Cited Count:
WoS CC Cited Count: 7
SCOPUS Cited Count: 7
ESI Highly Cited Papers on the List: 0 Unfold All
WanFang Cited Count:
Chinese Cited Count:
30 Days PV: 3
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