SIAM Journal on Control and Optimization, Volume 59, Issue 2, Page 906-930, January 2021.
We develop the compactification method to prove the existence of an optimal control for multidimensional stochastic processes with regime-switching. We consider separately the situations with and without state constraints. Three kinds of control policies are studied in this work: the classical controls on the drifts, the singular controls, and the controls on the transition rates of switching processes. Based on the existence of the optimal controls, the dynamic programming principle is also established.

中文翻译：

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切换条件下随机过程的无限视界最优奇异控制问题

SIAM控制与优化杂志，第59卷，第2期，第906-930页，2021年1月。
我们开发了压紧方法，以证明存在用于状态切换的多维随机过程的最优控制的存在。我们分别考虑有和没有国家约束的情况。本文研究了三种控制策略：漂移的经典控制，奇异控制和切换过程的过渡速率控制。基于最优控制的存在，建立了动态​​规划原理。