Mixed $\mathcal{H}_2/\mathcal{H}_\infty$-Policy Learning Synthesis

TL;DR

This paper introduces a robust, model-free control policy synthesis method using mixed $\\mathcal{H}_2/\\\mathcal{H}_\\infty$ techniques, leveraging stochastic calculus to improve stability and robustness in control systems.

Contribution

It presents a novel approach combining stochastic calculus with Riccati equations for robust control policy learning in a model-free setting.

Findings

Successfully synthesizes robust control policies in continuous-time systems.

Provides a unified, data-driven framework simplifying existing methods.

Demonstrates improved stability and robustness in control applications.

Abstract

A robustly stabilizing optimal control policy in a model-free mixed $\mathcal{H}_2/\mathcal{H}_\infty$-control setting is here put forward for counterbalancing the slow convergence and non-robustness of traditional high-variance policy optimization (and by extension policy gradient) algorithms. Leveraging It\^{o}'s stochastic differential calculus, we iteratively solve the system's continuous-time closed-loop generalized algebraic Riccati equation whilst updating its admissible controllers in a two-player, zero-sum differential game setting. Our new results are illustrated by learning-enabled control systems which gather previously disseminated results in this field in one holistic data-driven presentation with greater simplification, improvement, and clarity.