Overlapping internal boundary control of lane-free automated vehicle traffic

Lane-free vehicle driving has been recently proposed for connected automated vehicles on highways or arterials. Lane-free traffic implies that incremental changes of the road width lead to corresponding incremental changes of traffic flows and capacity. In these conditions, internal boundary control (IBC) was proposed for flexible sharing of the total road width and capacity among the two traffic directions of the highway in real-time in order to maximize the cross-road infrastructure utilization and minimize congestion and delays. Centralized solutions , e.g. LQ (linear quadratic) regulators, requiring information from the whole highway stretch under consideration, have already been proposed, which, however, may be cumbersome for long highways with respect to the offline controller design effort; the extent of real-time communications; and the physical system architecture. This paper investigates two different overlapping decentralized control schemes for IBC in lane-free automated vehicle traffic. The first approach is based on a contractible controller, which is designed and employed in a decomposed way, for each subsystem of an extended highway system. In the second approach, the overall discrete-time LQ control problem is transformed into a linear matrix inequalities (LMI) problem. After selecting the overlapping feedback structure and solving the overall LMI problem, the correspondingly structured gain matrix is obtained, enabling a decentralized overlapping control deployment in real-time. Simulation investigations, involving a realistic highway stretch and demand scenarios, demonstrate that the proposed decentralized regulators are almost as efficient as the centralized control solutions for the problem at hand.