Sampling-based approximation of the viability kernel for high-dimensional linear sampled-data systems
Sampling-based approximation of the viability kernel for high-dimensional linear sampled-data systems
复制标题
高维线性采样数据系统的生存核的基于采样的近似
DOI：
--
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
C. Tomlin
中科院分区：
文献类型：
--
作者：
J. Gillula;Shahab Kaynama;C. Tomlin
在设计网络物理系统时，人们经常需要满足系统来满足硬输入和状态限制。这样做的一种方法是计算可行性内核，这是存在控制信号的状态空间子集，该状态空间的子集保证在某个时间范围内将系统保持在约束之内。在本文中，我们提出了一种新的方法，用于使用基于采样的算法来近似线性采样数据系统的可行性内核，该算法通过其构造提供了可扩展性和准确性之间的直接权衡。我们还证明算法是正确的，其收敛属性是最佳的，并在一个简单的示例中进行了证明。最后，我们简要描述了由于空间限制而省略的其他结果。
Proving that systems satisfy hard input and state constraints is frequently desirable when designing cyber-physical systems. One method for doing so is to compute the viability kernel, the subset of the state space for which a control signal exists that is guaranteed to keep the system within the constraints over some time horizon. In this paper we present a novel method for approximating the viability kernel for linear sampled-data systems using a sampling-based algorithm, which by its construction offers a direct trade-off between scalability and accuracy. We also prove that the algorithm is correct, that its convergence properties are optimal, and demonstrate it on a simple example. We conclude by briefly describing additional results which are omitted due to space constraints.