{"ID":2870590,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.13446","arxiv_id":"2509.13446","title":"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 $i$ 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.","short_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 par...","url_abs":"https://arxiv.org/abs/2509.13446","url_pdf":"https://arxiv.org/pdf/2509.13446v1","authors":"[\"Addie McCurdy\",\"Emily Jensen\"]","published":"2025-09-16T18:27:15Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"eess.SY\"]","methods":"[]","has_code":false}