Controller Reduction for Nonlinear Systems by Generalized Differential Balancing

TL;DR

This paper develops computationally feasible nonlinear controller reduction methods using generalized differential balancing, extending previous approaches to include LQG and H-infinity balancing with stability guarantees.

Contribution

It introduces GD LQG and H-infinity balancing for nonlinear systems, providing stability conditions and relaxation to linear matrix inequalities.

Findings

GD H-infinity balancing ensures exponential stability under certain conditions

Methods are relaxable to linear matrix inequalities

Provides a systematic approach for nonlinear controller reduction

Abstract

In this paper, we aim at developing computationally tractable methods for nonlinear model/controller reduction. Recently, model reduction by generalized differential (GD) balancing has been proposed for nonlinear systems with constant input-vector fields and linear output functions. First, we study incremental properties in the GD balancing framework. Next, based on these analyses, we provide GD LQG balancing and GD $H_\infty$-balancing as controller reduction methods for nonlinear systems by focusing on linear feedback and observer gains. Especially for GD $H_\infty$-balancing, we clarify when the closed-loop system consisting of the full-order system and a reduced-order controller is exponentially stable. All provided methods for controller reduction can be relaxed to linear matrix inequalities.