Model uncertainty poses a significant challenge to the implementation of safety-critical control systems. With this as motivation, this paper proposes a safe control design approach that guarantees the robustness of nonlinear feedback systems in the presence of matched or unmatched unmodelled system dynamics and external disturbances. Our approach couples control barrier functions (CBFs) with a new uncertainty/disturbance estimator to ensure robust safety against input and state-dependent model uncertainties. We prove upper bounds on the estimator's error and estimated outputs. We use an uncertainty estimator-based composite feedback control law to adaptively improve robust control performance under hard safety constraints by compensating for the matched uncertainty. Then, we robustify existing CBF constraints with this uncertainty estimate and the estimation error bounds to ensure robust safety via a quadratic program (CBF-QP). We also extend our method to higher-order CBFs (HOCBFs) to achieve safety under unmatched uncertainty, which causes relative degree differences with respect to control input and disturbance. We assume the relative degree difference is at most one, resulting in a second-order cone (SOC) condition. The proposed robust HOCBFs method is demonstrated in a simulation of an uncertain elastic actuator control problem. Finally, the efficacy of our method is experimentally demonstrated on a tracked robot with slope-induced matched and unmatched perturbations.

翻译：模型不确定性对安全关键控制系统的实现构成了重大挑战。为此，本文提出一种安全控制设计方法，该方法能够保证非线性反馈系统在存在匹配或非匹配未建模系统动力学及外部扰动时的鲁棒性。本方法将控制障碍函数与一种新的不确定性/扰动估计器相结合，以确保针对输入和状态依赖型模型不确定性的鲁棒安全性。我们证明了估计器误差和估计输出的上界。采用基于不确定性估计器的复合反馈控制律，在严格安全约束下通过补偿匹配不确定性来自适应提升鲁棒控制性能。随后，利用该不确定性估计及其误差界对现有CBF约束进行鲁棒化处理，通过二次规划实现鲁棒安全性。我们将该方法扩展到高阶控制障碍函数，以在非匹配不确定性下（这会导致控制输入和扰动之间存在相对度差异）实现安全控制。假设相对度差异至多为1，从而得到二阶锥条件。通过一个不确定弹性致动器控制问题的仿真验证了所提出的鲁棒HOCBF方法。最后，通过履带机器人上由斜坡引发的匹配与非匹配扰动的实验，证明了该方法的有效性。