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.

Key words: ARZ traffic flow model, Time-delay boundary control, ISS-Lyapunov function, Input-to-state stability