论文标题
用于约束非线性动力学系统的基于图的不变设置算法的有效实现
An efficient implementation of graph-based invariant set algorithm for constrained nonlinear dynamical systems
论文作者
论文摘要
基于图形的不变集（GIS）算法是一种基于集合的技术，用于计算最大的（相对于包含）控制不变的一般离散时间非线性非线性动力学系统。但是，就像非线性系统的其他不变设置算法一样，在计算控件不变设置时，GIS算法可能需要大量资源。这将其适用性限制在更高维系统中。在这项工作中，我们提出了用于一般离散时间受控非线性系统的GIS算法的改进，有效的实现。我们首先通过广泛的分析确定瓶颈，然后提供补救程序以改善GIS算法的实施。具体而言，我们使用基于机器学习的算法开发了一种自适应细分方案，以降低细胞生长速率并平行图形构造步骤。我们使用数值示例广泛地证明了改进的GIS算法的性能，并将结果与标准GIS算法的结果进行比较。结果表明，自适应细分和并行化分别提高了算法的速度约为8倍和3倍，而标准GIS算法的速度分别提高了算法。
The graph-based invariant set (GIS) algorithm is a promising set-based technique for computing the largest (with respect to inclusion) control invariant set of general discrete-time nonlinear dynamical systems. However, like other invariant set algorithms for nonlinear systems, the GIS algorithm may require a lot of resources when computing the control invariant set. This limits its applicability to higher dimensional systems. In this work, we present an improved and efficient implementation of the GIS algorithm for general discrete-time controlled nonlinear systems. We first identify the bottlenecks through extensive analysis, and then provide remedial procedures to improve the implementation of the GIS algorithm. Specifically, we developed an adaptive subdivision scheme using a supervised machine learning-based algorithm to reduce the cell growth rate and parallelize the graph construction step. We extensively demonstrate the performance of the improved GIS algorithm using a numerical example and compare the result to that of the standard GIS algorithm. The results show that the adaptive subdivision and the parallelization improved the speed of the algorithm by about 8x and 3x respectively, that of the standard GIS algorithm.
