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arXiv · 2203.11177

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

Bin Hu·Yang Zheng
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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.

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Bin Hu, Yang Zheng. 2022-03-21. Connectivity of the Feasible and Sublevel Sets of Dynamic Output Feedback Control with Robustness Constraints. https://doi.org/10.1109/lcsys.2022.3188008

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