2024/10/30 by Lanzetti, Nicolas, Terpin, Antonio, Dörfler, Florian · 1 citation
#FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2410.22826
We prove that output-feedback linear policies remain optimal for solving the Linear Quadratic Gaussian regulation problem in the face of worst-case process and measurement noise distributions when these are independent, stationary, and known to be within a radius (in the Wasserstein sense) to some reference zero-mean Gaussian noise distributions. Additionally, we establish the existence of a Nash equilibrium of the zero-sum game between a control engineer, who minimizes control cost, and a fictitious adversary, who chooses the noise distributions that maximize this cost. For general (possibly non-Gaussian) reference noise distributions, we establish a quasi closed-form solution for the worst-case distributions against linear policies. Our work provides a less conservative alternative compared to recent work in distributionally robust control.