Fast Model Predictive Control for Urban Road Networks via MILP

Abstract

Abstract-In this paper, an advanced control strategy, i.e. Model Predictive Control (MPC), is applied to control and coordinate urban traffic networks. However, due to the nonlinearity of the prediction model, the optimization of MPC is a nonlinear non-convex optimization problem. In this case, the online computational complexity becomes a big challenge for the MPC controller, if it is implemented in real-life traffic network. To overcome this problem, the on-line optimization problem is reformulated into a Mixed-Integer Linear Programming (MILP) optimization problem, so as to increase the real-time feasibility of the MPC control strategy. The new optimization problem can be solved very efficiently by existing MILP solvers, and the global optimum of the problem is guaranteed. Moreover, we propose an approach to reduce the complexity of the MILP optimization problem even further. The simulation results show that the MILPbased MPC controllers can reach the same performance, but the time taken to solve the optimization becomes only a few seconds, which is a significant reduction compared with the time required by the original MPC controller.Index Terms-Urban traffic network control, Model predictive control, Urban traffic modeling.

Optimal Perimeter Control for Two Urban Regions With Macroscopic Fundamental Diagrams: A Model Predictive Approach

“…In addition, the performance of the MPC controller that encounters unbiased and biased noise in the demand is investigated. Example 1 with high unbiased noise in the demand (σ ij = 0.5, i, j = 1, 2), see (27), is illustrated in Fig. 9.…”

“…A receding horizon framework has been used for optimization in different traffic control problems, for example, ramp metering of freeway networks in [21] and [22], variable speed limits and route guidance for freeway networks in [23] and [24], signal control for large-scale urban networks in [25]- [27], and mixed urban and freeway networks in [28]. The open-loop optimization in the traffic MPC models, for example, in [23] and [24], uses a direct simultaneous method to transcript it into a finitedimensional nonlinear programming through the discretization of both control and state variables, whereas in [22] and [26], a feasible direction algorithm is utilized to solve the open-loop optimization problem.…”

Optimal Hybrid Perimeter and Switching Plans Control for Urban Traffic Networks

“…Therefore, a closed-loop optimal control scheme is needed to consider the errors between the plant and the model, and also the disturbances, e.g., variations in the expected demands that might affect the system (the differences between the model and the plant will be discussed in details later). Among these schemes is the MPC framework, which has been widely used for different traffic control purposes [23]- [28]. The MPC controller determines the optimal control inputs in a receding horizon manner, meaning that at each time step, an objective function is optimized over a prediction horizon of N p steps and a sequence of optimal control inputs are derived.…”

Cooperative traffic control of a mixed network with two urban regions and a freeway

“…ramp metering of freeway networks in Bellemans et al (2006), variable speed limits and route guidance for freeway networks in Kotsialos et al (2002) and Hegyi et al (2005a,b), signal control for large-scale urban networks in Gartner et al (2002), Aboudolas et al (2010), and Lin et al (2011), and mixed urban and freeway networks in van den Berg et al (2007). A historical survey for industrial applications (other than traffic control) of MPC can be found in Qin and Badgwell (2003), while theoretical issues of MPC can be found in Garcia et al (1989), Camacho and Bordons (1999), and Mayne et al (2000).…”