The problem of optimally controlling one-dimensional diffusion processes until they enter a given stopping set is extended to include Markov regime switching. The optimal control problem is presented by making use of dynamic programming. In the case where the Markov chain has two states, the optimal homotopy analysis method (OHAM) is used to obtain an analytical approximation of the value function, which is compared to the finite difference approximation with successive updates of the nonlinear and coupling terms. As an example, the method is applied to controlled population growth with regime switching.

中文翻译：

---

具有条件切换的马尔可夫过程的线性二次高斯归巢及其在人口增长/衰减控制中的应用

最优控制一维扩散过程直到它们进入给定的停止集的问题扩展到包括马尔可夫状态切换。利用动态规划提出了最优控制问题。在马尔可夫链具有两个状态的情况下，使用最佳同伦分析方法（OHAM）获得值函数的解析逼近，将其与有限差分逼近进行比较，并逐步更新非线性项和耦合项。作为示例，该方法被应用于通过体制转换来控制人口增长。