Guaranteed Stabilization and Safety of Nonlinear Systems via Sliding Mode Control

We study simultaneous stabilization and safety for nonlinear affine systems by unifying the control Lyapunov function (CLF) and control barrier function (CBF). With the sliding mode control, we develop a CLF-CBF control strategy in joint and switching forms based on a general and a particular class of sliding mode manifolds, respectively. Then, the sufficient conditions on the parameters that achieve the stabilization and safety objectives simultaneously are provided. These conditions are less conservative than the conditions required by the existing quadratic programming methods, where both CLF and CBF constraints need to be satisfied for all time. Finally, numerical simulations are conducted to verify the effectiveness and superiority of our proposed method.