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

Abstract

In a complex real-time operating environment, external disturbances and uncertainties adversely affect the safety, stability, and performance of dynamical systems. This paper presents a robust stabilizing safety-critical controller synthesis framework with control Lyapunov functions (CLFs) and control barrier functions (CBFs) in the presence of disturbance. A highgain input observer method is adapted to estimate the timevarying unmodelled dynamics of the CBF with an error bound using the first-order time derivative of the CBF. This approach leads to an easily tunable low-order disturbance estimator structure with a design parameter as it utilizes only the CBF constraint. The estimated unknown input and associated error bound are used to ensure robust safety and exponential stability by formulating a CLF-CBF quadratic program. The proposed method is applicable to both relative degree one and higher relative degree CBF constraints. The efficacy of the proposed approach is demonstrated using a numerical simulations of an adaptive cruise control system and a Segway platform with an external disturbance.

Disturbance Observer-based Robust Control Barrier Functions

“…) Define e ψ ≜ ψ(x, u)I n − ∂β ∂x as the "approximation error" induced by approximately solving (11) using β designed in (13b). Intuitively, from (15) one can see that if x is very close to x, e ψ would be negligible. Note that the influence of e ψ will be eliminated by ṙ as shown in the following analysis.…”

“…To reduce the adverse effects of disturbances/uncertainties on system performance, several works integrating disturbance/uncertainty estimation and compensation techniques into the CBF-QP framework have been proposed recently [14], [15], [16], [17]. In our previous work [14], the Disturbance Observer (DOB) presented in [18] was incorporated into the CBF-QP framework for the first time.…”