Robust Gain-Scheduled Continuous-Time Linear Quadratic Regulator for Mixed-Traffic Freeways: A Multi-Class Cell Transmission Model Approach

Advanced freeway tra c control strategies often rely on online optimization, which can be computationally intensive and limit their real-time applicability on large-scale networks. This study proposes a computationally e cient alternative: a linear parameter-varying gain-scheduled continuous-time linear quadratic regulator (GS–CT–LQR) to coordinate ramp metering (RM) and variable speed limiting (VSL) on mixed-tra c freeways. The approach uses a set of pre-computed feedback gains, derived from a multi-class cell transmission model, which are scheduled online based on real-time conditions like Cooperative Adaptive Cruise Control (CACC) market penetration, demand, and congestion state. A single quadratic Lyapunov function certifies uniform exponential stability and provides an input-to-state stability bound. The controller is comparatively evaluated on an 11 km corridor with measured demand in a comprehensive microsimulation study against baselines including no control, ALINEA, H1, and a model predictive controller. Across 25 to 75% penetration, the GS–CT–LQR improves throughput and average travel time, lowers CO2 emissions, and produces significantly smoother control actuation. It demonstrates superior robustness in stress tests involving demand surges, penetration drift, and measurement noise, all while achieving a median perupdate latency of just 0:13 ms on commodity hardware. The results confirm that the proposed approach o ers a practical and stable solution for real-time freeway tra c control, delivering the benefits of an adaptive strategy without the burden of online optimization.