Verification and Control for Finite-Time Safety of Stochastic Systems via Barrier Functions
Verification and Control for Finite-Time Safety of Stochastic Systems via Barrier Functions
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DOI：
10.1109/ccta.2019.8920407
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发表时间：
2019-05
期刊：
影响因子：
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通讯作者：
Cesar Santoyo;Maxence Dutreix;S. Coogan
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文献类型：
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作者：
Cesar Santoyo;Maxence Dutreix;S. Coogan
研究了有限时间范围内随机动力系统的安全性问题。我们使用随机势垒函数作为一种手段来量化系统在有限时间内退出给定状态空间安全区域的概率。为了有效的数值计算，将一个限制系统的无穷小生成器的屏障证书条件重新定义为一个平方和优化问题，从而限制了屏障函数在时间范围内的期望值。与以前的工作不同，提议的证书条件包括无限小生成器上的状态依赖边界，从而允许更严格的概率边界。此外，对于漂移动力学为仿射控制的随机系统，我们提出了一种合成多项式状态反馈控制器的方法，该方法可以达到指定的安全概率。给出了两个案例，作为基准并说明了我们的方法的性能。
This paper studies the problem of enforcing safety of a stochastic dynamical system over a finite time horizon. We use stochastic barrier functions as a means to quantity the probability that a system exits a given safe region of the state space in finite time. A barrier certificate condition that bounds the infinitesimal generator of the system, and hence 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 bound on the infinitesimal generator, allowing for tighter probability bounds. Moreover, for stochastic systems for which the drift dynamics are affine-in-control, we propose a method for synthesizing polynomial state feedback controllers that achieve a specified probability of safety. Two case studies are presented that benchmark and illustrate the performance of our method.