A Funnel-Based Framework for Quantitative Safety Metric Construction and Safety-Metric-Driven Control Synthesis of Automatic Carrier Landing Systems

Current research on Automatic Carrier Landing Systems (ACLSs) primarily focuses on guidance and control performance metrics. However, safety metrics that quantitatively characterize the safe region of ACLSs are equally crucial for guaranteeing safe landings, since safe and precise go-around decisions can only be made when the safe region is explicitly known. Therefore, this paper proposes a funnel-based framework that constructs quantitative safety metrics for making go-around decisions and quantitatively evaluating the safety of ACLSs. Additionally, safety-metric-driven control synthesis can be conducted to optimize controller parameters to maximize the safe region, i.e., to improve the safety of ACLSs. Specifically, the terminal landing requirements are formulated as a terminal set. Then, under the closed-loop dynamics with actuator saturation constraints and environmental disturbances, a funnel is constructed by sum-of-squares programming. Owing to its invariance property, all closed-loop trajectories starting inside the funnel converge to the terminal set, i.e., the terminal landing requirements are satisfied, and thus, the funnel serves as the safe region throughout the landing process. Furthermore, an online go-around decision rule is derived by checking whether the current state lies inside the offline-computed funnel. Simulation results validate the capability of the proposed framework to guarantee safe landings and further confirm its effectiveness under deck motion disturbance. Moreover, the funnel can serve as a larger safe region in the multi-dimensional state space than existing approaches based on a single state dimension, while constructing quantitative safety metrics for evaluating the safety of ACLSs. Finally, safety-metric-driven control synthesis demonstrates its ability to optimize controller parameters toward maximizing the safe region.