Reachability analysis of multi-affine systems
Reachability analysis of multi-affine systems
复制标题
多仿射系统的可达性分析
DOI：
10.1177/0142331208097838
复制
发表时间：
2006
影响因子：
1.8
通讯作者：
C. Belta
中科院分区：
文献类型：
--
作者：
Marius Kloetzer;C. Belta
我们提出了一个计算上有吸引力的技术来研究矩形区域的可达性的轨迹连续多仿射系统。该方法是迭代的。在每一步中，产生更精细的分区和过近似初始系统的可达性的有限子。我们利用一些凸性质的多仿射函数的矩形，以表明在每一步的商的建设只需要评估的向量场的所有顶点的集合中的所有矩形的分区，并找到一组有限的标量仿射函数的根。该方法可用于生化网络，飞机和水下航行器的形式化分析，其中多仿射模型被广泛使用。
We present a computationally attractive technique to study the reachability of rectangular regions by trajectories of continuous multi-affine systems. The method is iterative. At each step, finer partitions and finite quotients that over-approximate the reachability properties of the initial system are produced. We exploit some convexity properties of multi-affine functions on rectangles to show that the construction of the quotient at each step requires only the evaluation of the vector field at the set of all vertices of all rectangles in the partition and finding the roots of a finite set of scalar affine functions. This methodology can be used for formal analysis of biochemical networks, aircraft and underwater vehicles, where multi-affine models are widely used.