VSL Control with Monotone Traffic Model Bounds Based on T-norms

Paper i proceeding, 2026

In this paper, we propose a generic first-order traffic modeling framework based on cumulative vehicle numbers and t-norm operators, unifying several classical and kinetic traffic flow models within a common structure. Exploiting the monotonicity and cooperativeness properties of the resulting system, we construct simplified lower- and upper-bound dynamic models in order to enclose the trajectories of more complex and potentially unknown traffic dynamics. These bound systems enable designing Variable Speed Limits control laws with formal guarantees despite model uncertainty. We develop two control strategies: a simple proportional (myopic, approximate optimal) feedback controller and a minimum-time controller derived using the Pontryagin Maximum Principle. Both controllers are shown to preserve system monotonicity and to effectively reduce traffic density inhomogeneity. Numerical simulations demonstrate that the proposed approach accelerates congestion dissipation, while requiring very limited model information. The proposed framework introduces a systematic and analytically tractable approach to robust Variable Speed Limits control, using monotone system theory to define bounds to uncertain kinetic traffic flow models.