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 enable the efficient computation of control inputs during online execution, we provide 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：本文考虑在模型不确定的情况下执行动态系统的安全和稳定; 安全性和稳定性限制可分别使用控制屏障功能(CBF)和Lyapunov控制功能(CLF)加以规定。为了考虑到模型的不确定性,通常会考虑制约的稳健和概率配方。然而,这需要已知的错误界限或模型不确定性的已知分布,由此产生的配方可能受到过度保守或过度信任的影响。在本文件中,我们假定只有一套有限的模型参数不确定性样本,并制订一套分配上稳健的、机会限制的、与CFF安全和CLF稳定性保证结合的程序(DRCCP)。为了在网上执行时能够有效地计算控制投入,我们提供了重新拟订刚果民主共和国控制控制线作为第二阶锥形方案(SOLCP)。我们的配方是以适应性航行控制为例,比1个基准的CLF-CFF四方规划方法,2个假设系统不确定性的已知错误界限的稳健方法,3个假设一种机会限制办法,假设已知的Gaussian进程不确定性的分布。