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PreprintCC BY-NC-ND 4.0arXiv

LQG solution for POMDP without estimating states: A minimum variance approach

  • Ranjan Sarkar
  • Prabhat K. Mishra
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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.

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Cite

BibTeXRIS
BibTeX
@misc{sarkar2026solution,
  title = {{LQG solution for POMDP without estimating states: A minimum variance approach}},
  author = {Ranjan Sarkar and Prabhat K. Mishra},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2607.12135},
  eprint = {2607.12135},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.12135},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - LQG solution for POMDP without estimating states: A minimum variance approach
AU  - Ranjan Sarkar
AU  - Prabhat K. Mishra
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2607.12135
UR  - https://arxiv.org/abs/2607.12135
AB  - 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.
ER  -