LQG solution for POMDP without estimating states: A minimum variance approach
arXiv:2607.12135
The paper proposes a method to design a Linear Quadratic Gaussian controller for discrete-time linear systems with noisy and incomplete measurements that avoids explicit state estimation, using a minimum‑variance formulation that expresses the control input directly in terms of past measurements and inputs.
Abstract
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.