Binary optimal control by trust-region steepest descent
提出一种信赖域最速下降法，用于处理控制函数为二元可积函数的动态最优控制问题，通过将控制函数视为可测集的指示函数并利用拓扑梯度函数的子水平集进行集合值调整，理论证明该方法在离散化和截断误差下仍能达到渐近平稳性，并求解了常微分和偏微分方程约束的最优控制问题及拓扑优化问题。
Abstract We present a trust-region steepest descent method for dynamic optimal control problems with binary-valued integrable control functions. Our method interprets the control function as an indicator function of a measurable set and makes set-valued adjustments derived from the sublevel sets of a topological gradient function. By combining this type of update with a trust-region framework, we are able to show by theoretical argument that our method achieves asymptotic stationarity despite possible discretization errors and truncation errors during step determination. To demonstrate the practical applicability of our method, we solve two optimal control problems constrained by ordinary and partial differential equations, respectively, and one topological optimization problem.