Combining Control Lyapunov and Barrier Functions for constrained stabilization of nonlinear systems

In combination with Control Lyapunov and Control Barrier Functions (CLF and CBF), Quadratic Programming (QP) has been considered for control design for nonlinear system and has been successfully applied to robotic and automotive systems. This approach could be considered an extension of the CLF based point-wise minimum norm controller to constrained nonlinear systems. In this paper we modify the original QP problem in a way that guarantees local asymptotic stability under the standard (minimal) assumptions on the CLF and CBF. We also remove the assumption that the CBF has uniform relative degree one. The two design parameters of the new QP setup allow us to control how aggressive the resulting control law is when trying to satisfy the two control objectives. The paper presents the controller in a closed form making it unnecessary to solve the QP problem on line and facilitating the analysis that actually led to the final form of the QP problem presented here.