Linear-Quadratic regulators for internal boundary control of lane-free automated vehicle traffic

Lane-free vehicle movement has been recently proposed for connected automated vehicles (CAV) due to various potential advantages. One such advantage stems from the fact that incremental changes of the road width in lane-free traffic lead to corresponding incremental changes of the traffic flow capacity. Based on this property, the concept of internal boundary control was recently introduced to flexibly share the total road width and capacity among the two traffic directions of a highway in real-time, in response to the prevailing traffic conditions, so as to maximize the cross-road (both directions) infrastructure utilization. Feedback-based Linear-Quadratic regulators with or without Integral action (LQI and LQ regulators) are appropriately developed in this paper to efficiently address the internal boundary control problem. Simulation investigations, involving a realistic highway stretch and different demand scenarios, demonstrate that the proposed simple regulators are robust and similarly efficient as an open-loop nonlinear constrained optimal control solution, while circumventing the need for accurate modelling and external demand prediction