In this note we develop the theory of the quantum Pontryagin principle for continuous measurements and feedback. The analysis is carried out under the assumption of compatible events in the output channel. The plant is a quantum system, which generally is in a mixed state, coupled to a continuous measurement channel. The Pontryagin Maximum Principle is derived in both the Schr\"{o}dinger picture and Heisenberg picture, in particular in statistical moment coordinates. To avoid solving stochastic equations we derive a LQG scheme which is more suitable for control purposes.

中文翻译：

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连续测量下的量子庞特里亚金原理

在本笔记中，我们开发了用于连续测量和反馈的量子庞特里亚金原理的理论。分析是在假设输出通道中的兼容事件的情况下进行的。植物是一个量子系统，一般处于混合状态，耦合到连续的测量通道。在 Schr\"{o}dinger 图片和 Heisenberg 图片中，特别是在统计矩坐标中都导出了庞特里亚金极大值原理。为了避免求解随机方程，我们导出了更适合控制目的的 LQG 方案。