Computational synthesis of control barrier functions with applications in automotive lane keeping supervisory control

Abstract

The control barrier function (CBF) provides a good tool to design supervisory controllers for safety‐critical systems. However, constructing a CBF for a general nonlinear system is a challenging task. This paper presents a general CBF computational synthesis approach for nonlinear affine systems with state constraints and input constraints using sum‐of‐squares (SOS) programming. System dynamics and state constraints are approximated using polynomial functions, and the input constraints are approximated using linear functions. The CBF synthesis algorithm is presented step‐by‐step, and tricks to deal with potential numerical issues during the SOS optimizations are discussed. The proposed algorithm is applied to an automotive lane keeping application to synthesize a CBF, and a supervisory control based on this CBF is designed. The effectiveness and resilience of this CBF‐based supervisory control against disturbance are illustrated in simulation with a 14‐degree‐of‐freedom vehicle dynamics model. Results show that this CBF‐based supervisory control can improve the resilience of nominal controllers in automotive lane keeping applications.