Design of control strategies for robust dynamic routing in traffic networks

In this study, improved centralised and decentralised routing control strategies are developed based on minimisation of the worst-case queuing length. The centralised routing problem is formulated as an H_∞ optimal control problem to achieve a robust routing performance in the presence of unknown fast time-varying network delays. Then a decentralised routing problem is reformulated by treating every node as a single subsystem thereby yielding an algorithm that obtains the fastest route. In both cases, unconstrained solution is derived to design a delay-dependent H_∞ controller and expressed in terms of the feasibility of linear matrix inequality (LMI). Subsequently, physical constraints are imposed and added as LMIs. Salient features of the developed routing methodology including the increase of robustness against multiple unknown time-varying delays, and the enhancement of the scalability of the algorithm to large-scale traffic networks are delineated. Simulation results are presented to demonstrate the effectiveness and capabilities of the developed dynamic routing strategies.