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In this paper, we consider the problem of safe control synthesis of generalcontrolled nonlinear systems in the presence of bounded additive disturbances.Towards this aim, we first construct a governing augmented state space modelconsisting of the equations of motion of the original system, the integralcontrol law and the nonlinear disturbance observer. Next, we propose theconcept of Disturbance Observer based Integral Control Barrier Functions(DO-ICBFs) which we utilize to synthesize safe control inputs. Thecharacterization of the safe controller is obtained after modifying thegoverning integral control law with an additive auxiliary control input whichis computed via the solution of a quadratic problem. In contrast to priormethods in the relevant literature which can be unnecessarily cautious due totheir reliance on the worst case disturbance estimates, our DO-ICBF basedcontroller uses the available control effort frugally by leveraging thedisturbance estimates computed by the disturbance observer. By construction,the proposed DO-ICBF based controller can ensure state and input constraintsatisfaction at all times. Further, we propose Higher Order DO-ICBFs thatextend our proposed method to nonlinear systems with higher relative degreewith respect to the auxiliary control input. Finally, numerical simulations areprovided to validate our proposed approach.

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