# Sparse optimal control of networks with multiplicative noise via policy gradient

## TL;DR

This paper develops algorithms using policy gradient methods to design sparse controllers for complex networks affected by multiplicative noise, ensuring stability and optimality.

## Contribution

It introduces new algorithms that incorporate regularization into policy gradient methods for sparse control of noisy networked systems.

## Key findings

- Algorithms converge to effective sparse controllers
- Controllers stabilize large networked systems
- Regularization improves controller sparsity and performance

## Abstract

We give algorithms for designing near-optimal sparse controllers using policy gradient with applications to control of systems corrupted by multiplicative noise, which is increasingly important in emerging complex dynamical networks. Various regularization schemes are examined and incorporated into the optimization by the use of gradient, subgradient, and proximal gradient methods. Numerical experiments on a large networked system show that the algorithms converge to performant sparse mean-square stabilizing controllers.