Control Barrier Functions-based Semi-Definite Programs (CBF-SDPs): Robust Safe Control For Dynamic Systems with Relative Degree Two Safety Indices

Understand

In this draft article, we consider the problem of achieving safe control of a dynamic system for which the safety index or (control barrier function (loosely)) has relative degree equal to two.

• We consider parameter affine nonlinear dynamic systems and assume that the parametric uncertainty is uniform and known a-priori or being updated online through an estimator/parameter adaptation law.
• Under this uncertainty, the usual CBF-QP safe control approach takes the form of a robust optimization problem.
• Both the right hand side and left hand side of the inequality constraints depend on the unknown parameter.