Extension of switch point algorithm to boundary-value problems
Extension of switch point algorithm to boundary-value problems
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DOI：
10.1007/s10589-023-00530-y
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发表时间：
2023-07
影响因子：
2.2
通讯作者：
W. Hager
中科院分区：
文献类型：
--
作者：
W. Hager
在早期的论文（https：//doi.org/10.1137/21M1393315）中，开关点算法被开发用于求解最优控制问题，其解是奇异的或bang-bang的或奇异和bang-bang的，并且在解结构改变的时间点处具有有限数量的最优控制中的跳跃不连续性。这类控制问题被认为有一个给定的初始条件，但没有终端约束。该理论现在扩展到包括初始和终端约束的问题，这种结构经常出现在边值问题中。需要对理论进行实质性的修改，以处理这种更一般的设置。尽管如此，成本相对于切换点的导数仍然是切换点处汉密尔顿函数的跳跃。
In an earlier paper (https://doi.org/10.1137/21M1393315), the switch point algorithm was developed for solving optimal control problems whose solutions are either singular or bang-bang or both singular and bang-bang, and which possess a finite number of jump discontinuities in an optimal control at the points in time where the solution structure changes. The class of control problems that were considered had a given initial condition, but no terminal constraint. The theory is now extended to include problems with both initial and terminal constraints, a structure that often arises in boundary-value problems. Substantial changes to the theory are needed to handle this more general setting. Nonetheless, the derivative of the cost with respect to a switch point is again the jump in the Hamiltonian at the switch point.