Balanced Reduced-Order Models for Iterative Nonlinear Control of Large-Scale Systems

TL;DR

This paper introduces a framework for designing controllers for large-scale nonlinear systems by combining reduced-order models with iterative LQR, demonstrating effective control in numerical experiments.

Contribution

It develops a novel approach to create nonlinear reduced-order models using balanced truncation techniques for efficient control of high-dimensional systems.

Findings

ILQR produces good control on ROMs.

BT-ROM controllers outperform LQG-BT for very low dimensions.

Effective control demonstrated on nonlinear Burgers equation.

Abstract

We propose a new framework to design controllers for high-dimensional nonlinear systems. The control is designed through the iterative linear quadratic regulator (ILQR), an algorithm that computes control by iteratively applying the linear quadratic regulator on the local linearization of the system at each time step. Since ILQR is computationally expensive, we propose to first construct reduced-order models (ROMs) of the high-dimensional nonlinear system. We derive nonlinear ROMs via projection, where the basis is computed via balanced truncation (BT) and LQG balanced truncation (LQG-BT). Numerical experiments are performed on a semi-discretized nonlinear Burgers equation. We find that the ILQR algorithm produces good control on ROMs constructed either by BT or LQG-BT, with BT-ROM based controllers outperforming LQG-BT slightly for very low-dimensional systems.