An Extended Linear Quadratic Model Predictive Control Approach for Multi-Destination Urban Traffic Networks

Abstract

This paper extends an existing linear quadratic model predictive control (LQMPC) approach to multi-destination traffic networks, where the correct origin-destination (OD) relations are preserved. In the literature, the LQMPC approach has been presented for efficient routing and intersection signal control. The optimization problem in the LQMPC has a linear quadratic formulation that can be solved quickly, which is beneficial for a real-time application. However, the existing LQMPC approach does not preserve OD relations and thus may send traffic to wrong destinations. This problem is tackled by a heuristic method presented is this paper. We present two macroscopic models: 1) a non-linear route-specific model which keeps track of traffic dynamics for each OD pair and 2) a linear model that aggregates all route traffic states, which can be embedded into the LQMPC framework. The route-specific model predicts traffic dynamics and provides information to the LQMPC before the optimization and evaluates the optimal solutions after the optimization. The information obtained from the route-specific model is formulated as constraints in the LQMPC to narrow the solution space and exclude unrealistic solutions that would lead to flows that are inconsistent with the OD relations. The extended LQMPC approach is tested in a synthetic network with multiple bottlenecks. The simulation of the LQMPC approach achieves a total time spent close to the system optimum, and the computation time remains tractable.