  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-of-squares program and physics-based
modeling and optimization. A real-time quadratic program is posed to combine
the control barrier functions with the performance-based controllers, which can
be either expressed as control Lyapunov function conditions or as black-box
legacy controllers. In both cases, the resulting 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. The effectiveness of the control approach is
demonstrated by simulations in the industry-standard vehicle simulator Carsim.
