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)。为了便利在网上执行期间有效计算控制投入,我们提出重新拟订刚果民主共和国控制点,作为二级锥形方案(SOLCP)。我们是在适应性航行控制实例中评价我们的配方,比1个基准的CLF-CFF的二次规划方法,2个假设系统不确定性的已知错误界限的稳健方针,3个机会限制办法,假设已知的戈斯进程不确定性的分布。</s>