Approximation of reachable sets using optimal control and support vector machines
Approximation of reachable sets using optimal control and support vector machines
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DOI：
10.1016/j.cam.2016.06.015
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发表时间：
2014-12
期刊：
影响因子：
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通讯作者：
M. Rasmussen;J. Rieger;K. Webster
中科院分区：
文献类型：
--
作者：
M. Rasmussen;J. Rieger;K. Webster
我们提出并讨论了一种新的非线性控制系统可达集数值逼近的计算方法。它基于支持向量机算法，并将集合近似表示为在再现内核希尔伯特空间中选择的函数的子级集合。从某种意义上说，该方法可以被认为是 Baier、Gerdts 和 Xausa 最近开发的最优控制算法方法的扩展。对于选定的示例，以数字方式说明了该方法的收敛性。
We propose and discuss a new computational method for the numerical approximation of reachable sets for nonlinear control systems. It is based on the support vector machine algorithm and represents the set approximation as a sublevel set of a function chosen in a reproducing kernel Hilbert space. In some sense, the method can be considered as an extension to the optimal control algorithm approach recently developed by Baier, Gerdts and Xausa. The convergence of the method is illustrated numerically for selected examples.