A Scalable Procedure for $\mathcal{H}_{\infty}-$Control Design

TL;DR

This paper introduces a new scalable gradient-based method for $ive$-control design that uses algebraic Riccati equations and a novel step-size rule, demonstrating improved scalability and convergence on benchmark systems.

Contribution

It presents a novel gradient-based control design procedure combining Riccati equations with an innovative step-size rule, enhancing scalability over existing methods.

Findings

Demonstrates convergence on various benchmark systems.

Shows improved scalability compared to SDP-based algorithms.

Validates effectiveness through numerical experiments.

Abstract

This paper proposes a novel gradient based scalable procedure for $\mathcal{H}_{\infty}-$control design. We compute the gradient using algebraic Riccati equation and then couple it with a novel Armijo rule inspired step-size selection procedure. We perform numerical experiments of the proposed solution procedure on an exhaustive list of benchmark engineering systems to show its convergence properties. Finally we compare our proposed solution procedure with available semi-definite programming based gradient-descent algorithm to demonstrate its scalability.