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.

翻译：在前期论文（https://doi.org/10.1137/21M1393315）中，边界切换点算法被提出用于求解最优控制问题，该类问题的解为奇异型、bang-bang型或两者兼有，且最优控制在解结构发生变化的时点上存在有限个跳跃间断点。所考虑的这类控制问题具有给定初始条件，但无终端约束。现将其理论扩展至包含初始与终端双重约束的问题——这种结构常见于边值问题中。为应对这一更普遍的情形，需对原有理论进行实质性修改。然而，成本函数对切换点的导数仍然等于哈密顿量在切换点处的跃变量。