Disturbance Observer-based Robust Integral Control Barrier Functions for Nonlinear Systems with High Relative Degree

In this paper, we consider the problem of safe control synthesis of general controlled nonlinear systems in the presence of bounded additive disturbances. Towards this aim, we first construct a governing augmented state space model consisting of the equations of motion of the original system, the integral control law and the nonlinear disturbance observer. Next, we propose the concept of Disturbance Observer based Integral Control Barrier Functions (DO-ICBFs) which we utilize to synthesize safe control inputs. The characterization of the safe controller is obtained after modifying the governing integral control law with an additive auxiliary control input which is computed via the solution of a quadratic problem. In contrast to prior methods in the relevant literature which can be unnecessarily cautious due to their reliance on the worst case disturbance estimates, our DO-ICBF based controller uses the available control effort frugally by leveraging the disturbance estimates computed by the disturbance observer. By construction, the proposed DO-ICBF based controller can ensure state and input constraint satisfaction at all times. Further, we propose Higher Order DO-ICBFs that extend our proposed method to nonlinear systems with higher relative degree with respect to the auxiliary control input. Finally, numerical simulations are provided to validate our proposed approach.