Optimization controller synthesis using adaptive robust control Lyapunov and barrier functions for high-order nonlinear system

The control Lyapunov function (CLF)- and the control barrier function (CBF)-based control methods have been popularly studied to mediate the safety and stability requirements for the nonlinear control system. In this article, we propose a general adaptive robust control framework that can accommodate high-relative-degree constraints and matched and mismatched disturbances in the system dynamics while also avoiding the sharp increase in the time complexity and the conservatism of the controller, which is a challenging problem in current methods. An online adaptive estimation scheme is first presented to estimate the dynamics of matched and mismatched disturbances. Then an adaptive robust CLF (ARCLF) and an adaptive robust CBF (ARCBF) are proposed and integrated with a quadratic program (QP) to synthesize the general adaptive robust control framework, without adding any extra decision variables. The safety and the stability of the proposed method are also proved. Finally, the safe control problem of an underactuated unmanned surface vessel (UUSV) with matched and mismatched disturbances is solved to validate that the proposed method has less conservatism and better control performance compared with the existing methods.