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In a complex real-time operating environment, external disturbances anduncertainties adversely affect the safety, stability, and performance ofdynamical systems. This paper presents a robust stabilizing safety-criticalcontroller synthesis framework with control Lyapunov functions (CLFs) andcontrol barrier functions (CBFs) in the presence of disturbance. A high-gaininput observer method is adapted to estimate the time-varying unmodelleddynamics of the CBF with an error bound using the first-order time derivativeof the CBF. This approach leads to an easily tunable low order disturbanceestimator structure with a design parameter as it utilizes only the CBFconstraint. The estimated unknown input and associated error bound are used toensure robust safety and exponential stability by formulating a CLF-CBFquadratic program. The proposed method is applicable to both relative degreeone and higher relative degree CBF constraints. The efficacy of the proposedapproach is demonstrated using a numerical simulations of an adaptive cruisecontrol system and a Segway platform with an external disturbance.

Robust Safe Control Synthesis with Disturbance Observer-Based Control Barrier Functions