Correctness Guarantees for the Composition of Lane Keeping and Adaptive Cruise Control

This paper develops a control approach with correctness guarantees for the simultaneous operation of lane keeping and adaptive cruise control. The safety specifications for these driver assistance modules are expressed in terms of set invariance. Control barrier functions are used to design a family of control solutions that guarantee the forward invariance of a set, which implies satisfaction of the safety specifications. The control barrier functions are synthesized through a combination of sum-ofsquares program and physics-based modeling and optimization. A real-time quadratic program is posed to combine the control barrier functions with performance-based control Lyapunov functions, such that the generated feedback control guarantees the safety of the composed driver assistance modules in a formally correct manner. Importantly, the quadratic program admits a closed-form solution that can be easily implemented.