We study the problem of synthesizing a control strategy to enforce safety of affine-in-control stochastic dynamical systems over finite time horizons. We use stochastic control barrier functions to quantify the probability that a system exits a given safe region of the state space in finite-time and consider both continuous-time and discrete-time systems. A barrier certificate condition that bounds the expected value of the barrier function over the time horizon is recast as a sum-of-squares optimization problem for efficient numerical computation. Unlike prior works, the proposed certificate condition includes a state-dependent upper bound on the evolution of the expectation, allowing for tighter probability bounds. Two examples are presented.

我们研究综合控制策略以在有限的时间范围内加强仿射控制随机动态系统安全性的问题。我们使用随机控制屏障函数来量化系统在有限时间内退出状态空间给定安全区域的概率，并同时考虑连续时间系统和离散时间系统。将障碍证明条件限制在时间范围内的障碍证明条件，将其重铸为平方和优化问题，以进行有效的数值计算。与先前的工作不同，拟议的证书条件在期望的演变过程中包括与状态有关的上限，从而允许更严格的概率范围。给出两个例子。