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### 带干扰项的 ARZ 交通流模型的时滞控制与 ISS 稳定性

1. 中北大学数学学院 太原 030051
• 收稿日期:2023-05-31 修回日期:2024-01-30 出版日期:2024-08-26 发布日期:2024-07-26
• 通讯作者: *赵东霞, E-mail: zhaodongxia6@sina.com
• 作者简介:高彩霞, E-mail: 1519546532@qq.com
• 基金资助:
山西省基础研究计划(20210302123046);国家自然科学基金青年基金(12001343)

### The Delayed Control and Input-to-State Stability of ARZ Traffic Flow Model with Disturbances

Gao Caixia(),Zhao Dongxia*()

1. School of Mathematics, North University of China, Taiyuan 030051
• Received:2023-05-31 Revised:2024-01-30 Online:2024-08-26 Published:2024-07-26
• Supported by:
Fundamental Research Program of Shanxi Province(20210302123046);National Natural Science Foundation of China(12001343)

Abstract:

For the linearized ARZ traffic flow model, the existing literatures are usually based on the following assumptions: First, the equilibrium state of the system is exactly equal to the speed of free flow; Second, the traffic flow entering the upstream section is exactly equal to the mathematical expectation of traffic demand; Third, the boundary feedback doesn't consider the impact of time delay factors. In this paper, a PDE-PDE infinite-dimensional coupled closed-loop system with model drift term and boundary disturbance term is established without these constraints by combining the time-delay boundary control strategy. Specifically, the closed-loop system is transformed into an abstract evolution equation by using operator semigroup theory. The well-posedness of the closed-loop system is proved by combining the admissible theory of linear system solutions and control operators. The weighting ISS-Lyapunov function is constructed, and the input-to-state stability(ISS) of the closed-loop system is proved. The dissipative conditions of the feedback parameters are obtained. The effectiveness of the proposed controller and the feasibility of the parameter conditions are further verified by numerical simulation experiments.

• O231.4