Robust dynamic bus controls considering delay disturbances and passenger demand uncertainty

This paper proposes a robust dynamic control mechanism for bus transit system, taking account of variations in congestion delays and passenger demand, and combines bus holding and operating speed control strategies. By using a prespecified uncertainty set, we propose a state space model for bus motion with delay disturbances and passenger demand uncertainties. According to the Lyapunov function analysis method, we design a robust dynamic control based on the state-feedback scheme as the bus control to achieve the robust stability of the bus transit system, which effectively reduces the bus bunching phenomenon. Furthermore, we formulate a nonlinear optimal control problem to design the robust optimal bus control, which not only reduces the bus bunching, but also improves the schedule adherence and headway regularity of bus service lines. To handle the complexity of the nonlinear optimal control problem with uncertain parameters and disturbances, we reduce it to a convex optimization problem by the minimization of an upper bound on the objective function. The problem is solved in a polynomial time and satisfies the practical real time requirement. Numerical examples are presented to validate the effectiveness of the model and control methods.