2025/09/16 by McCurdy, Addie, Emily Jensen, Jensen, Emily
Computer Science · Engineering · #Adaptive Dynamic Programming Control #Extremum Seeking Control Systems #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2509.13446
openalex publication_date 2025/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.