Analysis of the optimization landscape of Linear Quadratic Gaussian (LQG) control

This paper revisits the classical Linear Quadratic Gaussian (LQG) control from a modern optimization perspective. We analyze two aspects of landscape LQG problem: (1) Connectivity set stabilizing controllers $$\mathcal {C}_n$$ ; and (2) Structure stationary points. It is known that similarity transformations do not change input-output behavior dynamic controller or cost. inherent symmetry by makes very rich. show The has at most path-connected components they are diffeomorphic under mapping defined transformation; There might exist many strictly suboptimal points cost function over controllable observable; (3) All observable globally optimal identical up to transformation. These results shed some light on performance analysis direct policy gradient methods for solving problem.