Risk-Aware Finite-Horizon Social Optimal Control of Mean-Field Coupled Linear-Quadratic Subsystems

TL;DR

This paper develops a novel risk-aware control framework for mean-field coupled linear-quadratic systems, emphasizing variability and skewness in disturbances, and introduces analytical tools to derive solutions from standard LQR methods.

Contribution

It introduces an alternative approach that reveals a family of matrices with useful properties, enabling the extraction of mean-field solutions from standard LQR solutions.

Findings

New analytical properties of matrix families for mean-field control

Effective extraction of coupled solutions from standard LQR

Enhanced risk-awareness in control of coupled systems

Abstract

We formulate and solve an optimal control problem with cooperative, mean-field coupled linear-quadratic subsystems and additional risk-aware costs depending on the covariance and skew of the disturbance. This problem quantifies the variability of the subsystem state energy rather than merely its expectation. In contrast to related work, we develop an alternative approach that illuminates a family of matrices with many analytical properties, which are useful for effectively extracting the mean-field coupled solution from a standard LQR solution.