Complete Decentralization of Linear Quadratic Gaussian Control for the Discrete Wave Equation
Abstract
The linear quadratic Gaussian (LQG) control problem for the linear wave equation on the unit circle with fully distributed actuation and partial state measurements is considered. An analytical solution to a spatial discretization of the problem is obtained. The main result of this work illustrates that for specific parameter values, the optimal LQG policy is completely decentralized, meaning only a measurement at spatial location is needed to compute an optimal control signal to actuate at this location. The relationship between performance and decentralization as a function of parameters is explored. Conditions for complete decentralization are related to metrics of kinetic and potential energy quantities and control effort.
Keywords
Cite
@article{arxiv.2509.13446,
title = {Complete Decentralization of Linear Quadratic Gaussian Control for the Discrete Wave Equation},
author = {Addie McCurdy and Emily Jensen},
journal= {arXiv preprint arXiv:2509.13446},
year = {2025}
}
Comments
7 pages, 4 figures, accepted for publication IEEE Conference on Decision and Control 2025