Connectivity of the Feasible and Sublevel Sets of Dynamic Output Feedback Control with Robustness Constraints

Abstract

This paper considers the optimization landscape of linear dynamic output feedback control with ${\mathcal{H}}_{\infty }$ robustness constraints. We consider the feasible set of all the stabilizing full-order dynamical controllers that satisfy an additional ${\mathcal{H}}_{\infty }$ robustness constraint. We show that this ${\mathcal{H}}_{\infty }$-constrained set has at most two path-connected components that are diffeomorphic under a mapping defined by a similarity transformation. Our proof technique utilizes a classical change of variables in ${\mathcal{H}}_{\infty }$ control to establish a subjective mapping from a set with a convex projection to the ${\mathcal{H}}_{\infty }$-constrained set. This proof idea can also be used to establish the same topological properties of strict sublevel sets of linear quadratic Gaussian (LQG) control and optimal ${\mathcal{H}}_{\infty }$ control. Our results bring positive news for gradient-based policy search on robust control problems.

Submitted to L-CSS and CDC 2022

References in corpus (1)

• Connectivity of the Feasible and Sublevel Sets of Dynamic Output Feedback Control with Robustness Constraints

Cited by in corpus (2)

• Connectivity of the Feasible and Sublevel Sets of Dynamic Output Feedback Control with Robustness Constraints
• Output-feedback Synthesis Orbit Geometry: Quotient Manifolds and LQG Direct Policy Optimization