# Escaping Locally Optimal Decentralized Control Polices via Damping

## TL;DR

This paper investigates how increasing damping in decentralized control systems causes local optima to merge into a single global optimum, simplifying the control design landscape.

## Contribution

It introduces a theoretical framework using hemi-continuity to analyze the evolution of local optima under damping and proves the elimination of spurious local solutions with large damping.

## Key findings

- Damping merges local solutions into the global solution.
- Large damping eliminates spurious local optima.
- Numerical examples illustrate complex trajectories and convergence.

## Abstract

We study the evolution of locally optimal decentralized controllers with the damping of the control system. Empirically it is shown that even for instances with an exponential number of connected components, damping merges all local solutions to the one global solution. We characterize the evolution of locally optimal solutions with the notion of hemi-continuity and further derive asymptotic properties of the objective function and of the locally optimal controllers as the damping becomes large. Especially, we prove that with enough damping, there is no spurious locally optimal controller with favorable control structures. The convoluted behavior of the locally optimal trajectory is illustrated with numerical examples.