A Control-Theoretic Approach for Scalable and Robust Traffic Density Estimation Using Convex Optimization

Monitoring and control of traffic networks represent alternative, inexpensive strategies to minimize congestion. As the number sensors is naturally constrained by budgetary requirements, real-time estimation flow in road segments that are not equipped with significant importance - thereby providing situational awareness guiding feedback strategies. To end, firstly we build a generalized model for stretched highways arbitrary ramp flows based on Lighthill Whitham Richards (LWR) model. Secondly, characterize function set corresponding nonlinearities present LWR model, use this characterization design robust state estimators (SE) highway segments. Specifically, show from derived models locally Lipschitz continuous analytical constants. Thirdly, derivation then incorporated through SE method given limited sensors, under impact process measurement disturbances unknown inputs. The estimator deriving convex semidefinite optimization problem. Finally, numerical tests showcasing applicability, scalability, robustness proposed large systems high magnitude disturbances, parametric uncertainty,