论文标题
分层域上最佳控制问题的值函数的近似
Approximation of the value function for optimal control problems on stratified domains
论文作者
论文摘要
在分层域定义的最佳控制问题中，动力学和运行成本可能在RN的子手机的有限结合上不连续。在[8，5]中，相应的值函数被表征为不连续的汉密尔顿 - 雅各比方程的唯一粘度解，可满足子序列上的其他粘度条件。在本文中，我们考虑了以前问题的半拉格朗日近似方案。依靠粘度解决方案理论中的经典稳定性参数，我们证明了方案与价值函数的收敛性。我们还提出了HJSD，这是我们为在两个和三个维度中分层域上的控制问题的数值解决方案开发的免费软件，在各个示例中显示了相对于经典连续框架可能出现的特定现象。
In optimal control problems defined on stratified domains, the dynamics and the running cost may have discontinuities on a finite union of submanifolds of RN. In [8, 5], the corresponding value function is characterized as the unique viscosity solution of a discontinuous Hamilton-Jacobi equation satisfying additional viscosity conditions on the submanifolds. In this paper, we consider a semi-Lagrangian approximation scheme for the previous problem. Relying on a classical stability argument in viscosity solution theory, we prove the convergence of the scheme to the value function. We also present HJSD, a free software we developed for the numerical solution of control problems on stratified domains in two and three dimensions, showing, in various examples, the particular phenomena that can arise with respect to the classical continuous framework.
