This paper considers enforcing safety and stability of dynamical systems in the presence of model uncertainty. Safety and stability constraints may be specified using a control barrier function (CBF) and a control Lyapunov function (CLF), respectively. To take model uncertainty into account, robust and chance formulations of the constraints are commonly considered. However, this requires known error bounds or a known distribution for the model uncertainty, and the resulting formulations may suffer from over-conservatism or over-confidence. In this paper, we assume that only a finite set of model parametric uncertainty samples is available and formulate a distributionally robust chance-constrained program (DRCCP) for control synthesis with CBF safety and CLF stability guarantees. To facilitate efficient computation of control inputs during online execution, we present a reformulation of the DRCCP as a second-order cone program (SOCP). Our formulation is evaluated in an adaptive cruise control example in comparison to 1) a baseline CLF-CBF quadratic programming approach, 2) a robust approach that assumes known error bounds of the system uncertainty, and 3) a chance-constrained approach that assumes a known Gaussian Process distribution of the uncertainty.

翻译：本文考虑了在存在模型不确定性的情况下确保动力系统的安全性与稳定性。安全性和稳定性约束可分别通过控制障碍函数（CBF）和控制李雅普诺夫函数（CLF）来指定。为了考虑模型不确定性，通常采用约束的鲁棒形式和机会形式。然而，这需要已知模型不确定性的误差界或分布，且所得形式可能过于保守或过度自信。本文假设仅可获得有限的一组模型参数不确定性样本，并基于CBF安全性和CLF稳定性保证，为控制综合建立了一个分布鲁棒机会约束规划（DRCCP）。为了便于在线执行时高效计算控制输入，我们将该DRCCP重新表述为二阶锥规划（SOCP）。所提出的方法在自适应巡航控制示例中进行了评估，并与以下方法进行对比：1）基线CLF-CBF二次规划方法；2）假设系统不确定性误差界已知的鲁棒方法；3）假设不确定性服从已知高斯过程分布的机会约束方法。