不依赖状态估计的LQG控制器，用最小方差方法直接设计控制输入。
LQG solution for POMDP without estimating states: A minimum variance approach
- 通过最小方差对偶性，将控制输入表示为测量值和历史输入的线性函数。
- 避免了显式状态估计，将原问题转化为可解的确定性优化。
- 适合需要低延迟、无状态估计开销的实时控制系统设计者。
本文研究离散时间线性时不变（LTI）系统在观测不完整且受噪声污染情况下的控制问题。重点在于设计一种不依赖显式状态估计的线性二次高斯（LQG）控制器。通过利用最小方差对偶性，该方法使当前控制输入可表示为可用测量值和先前施加输入的线性函数，从而将原问题转化为一个可处理的确定性优化问题。本文提供了该框架的理论依据，并通过数值实验验证了其实际有效性。
原文摘要 · Abstract (English)
This paper investigates the control of discrete-time linear time-invariant (LTI) systems subject to incomplete and corrupted measurements. Specifically, we focus on designing a Linear Quadratic Gaussian (LQG) controller without relying on explicit state estimation. By leveraging minimum variance duality, our approach allows the current control input to be represented as a linear function of available measurements and previously applied inputs, successfully reducing the task to a tractable deterministic optimization problem. We provide theoretical justification for this framework and demonstrate its practical effectiveness through numerical experiments.
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