Adaptive Safety Control of Nonlinearly Parameterized Systems via Logic-Based Switching

This paper investigates the problem of adaptive safety control for a class of nonlinearly parameterized systems. A novel adaptive safety control strategy for the problem studied is established to guarantee system safety, in which a logic switching mechanism is designed to replace parameter update law and a barrier function with a high relative degree with respect to the control input is considered. Also, a high-order parameterized control barrier function is introduced, which can accommodate nonlinearly parameterized systems of arbitrary relative degrees. The proposed strategy permits removal of two common restrictions in traditional adaptive safety control, in which a priori bound of unknown parameters is usually required to be known, or initial parameter estimation error must be within a known compact set, and the parameterization is restricted to a linear parameterization. Moreover, the proposed strategy is extended to high relative degree multiple safety constraints. Finally, two examples are provided to demonstrate the effectiveness of the proposed design strategy.