2025/05/16 by J. T. Scruggs, Jeffrey T. Scruggs, Scruggs, J. T.
Engineering · #Stability and Controllability of Differential Equations #Stability and Control of Uncertain Systems #Control and Stability of Dynamical Systems
paper · pdf · doi:10.48550/arxiv.2505.10811
We consider the \SetH2-optimal feedback control problem, for the case in which the plant is passive with bounded \SetL2 gain, and the feedback law is constrained to be output-strictly passive. We show that this problem distills to a convex, infinite-dimensional optimal control problem, in which the optimization domain is the Youla parameter for the closed-loop system. We devise truncated, finite-dimensional optimizations to find sub-optimal controllers, and lower bounds on the optimal objective. Furthermore we show that both these optimizations converge to the optimal objective of the original infinite-dimensional problem as their respective domains are increased. The idea is demonstrated on a simple vibration suppression example.