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Approximate Safety Verification and Control of Partially Observable Stochastic Hybrid Systems

机译:部分可观察的随机混合系统的近似安全验证和控制

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摘要

Assuring safety in stochastic hybrid systems is particularly difficult when only noisy or partial observations of the state are available. We first review a formulation of the probabilistic safety problem under partial hybrid observations as a dynamic program over an equivalent information state. Two methods for approximately solving the dynamic program are presented. The first approximates the hybrid system as a finite state Markov decision process, so that the information state is a probability mass function. The second method approximates an indicator function over the safe region using radial basis functions, to represent the information state as a Gaussian mixture. In both cases we discretize the hybrid observation process, then use point-based value iteration to under-approximate the safety probability and synthesize a safety-preserving control policy. We obtain error bounds and convergence results in both cases, assuming switched affine dynamics and additive Gaussian noise on the continuous states and observations. We compare the performance of the finite state and Gaussian mixture approaches on a simple numerical example.
机译:当仅对状态进行嘈杂或部分观察时,确保随机混合系统的安全性特别困难。我们首先回顾部分混合观测下概率安全问题的公式,将其作为在等效信息状态下的动态程序。提出了两种近似求解动态程序的方法。首先将混合系统近似为有限状态马尔可夫决策过程,因此信息状态为概率质量函数。第二种方法使用径向基函数对安全区域上的指标函数进行近似,以将信息状态表示为高斯混合。在这两种情况下,我们都将混合观测过程离散化,然后使用基于点的值迭代来将安全概率低估并合成安全保护的控制策略。假设在连续状态和观测条件下具有仿射动力学和加性高斯噪声,我们在两种情况下均获得误差范围和收敛结果。我们在一个简单的数值示例上比较了有限状态和高斯混合方法的性能。

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