Safety-Critical Disturbance Rejection Control of Nonlinear Systems With Unmatched Disturbances

Safety-critical control is significant for autonomous system applications where safety is an utmost concern. Control-barrier-function (CBF)-based control has shown its promising potential and power in delivering formal safe property of dynamic nonlinear systems. The presence of disturbances, whether from matched or unmatched channels, negatively impacts CBF-based control, leading to violations of formal safety guarantees and degraded control performance. In this article, a new safety-critical disturbance rejection control approach is proposed for nonlinear systems subject to unmatched disturbances. Owing to the naturally intractable mismatching condition, the disturbances and their high order derivatives could generate considerable negative impacts on not only the high order CBF but also the control Lyapunov function. To this end, an observer-based disturbance rejection CBF is proposed, delivering a new robust adaptive mechanism to deal with the disturbances. It is shown that by fully exploiting the disturbance estimates and adequately quantifying the impacts of estimation errors, the proposed approach provides attractive properties like formal robust safety guarantee and nominal control performance recovery under unmatched disturbances. Simulation results of path following of a drone suffering wind disturbances verify the benefits of the proposed solution in collision avoidance and retaining nominal safety performance.