Input design for the optimal control of networked moments

TL;DR

This paper develops an algorithm for optimally controlling the mean and variance of networked system states by designing input placements using projected gradient descent, considering constraints and system properties.

Contribution

It introduces a novel method combining state selection with gradient-based input design for controlling network moments.

Findings

Solutions related to eigenvalues of Gramian matrices.

Effective input placement strategies for moment control.

Algorithm achieves minimum cost control under constraints.

Abstract

We study the optimal control of the mean and variance of the network state vector. We develop an algorithm that uses projected gradient descent to optimize the control input placement, subject to constraints on the state that must be achieved at a given time threshold; seeking to design an input that moves the moment at minimum cost. First, we solve the state-selection problem for a number of variants of the first and second moment, and find solutions related to the eigenvalues of the systems' Gramian matrices. We then nest this state selection into projected gradient descent to design optimal inputs.