Output-Feedback Control of Nonlinear Systems using Control Contraction Metrics and Convex Optimization

TL;DR

This paper introduces an extension of control contraction metrics (CCMs) for nonlinear systems, enabling the design of output-feedback controllers via convex optimization and demonstrating the approach on a jet engine model.

Contribution

It extends CCM theory by establishing a duality between observer and controller problems and proves a separation principle for nonlinear control design.

Findings

Dual solutions for observer and controller problems can be obtained using LMIs.

A stabilizing output-feedback controller can be designed when solutions exist.

The method is validated on a nonlinear jet engine compressor model.

Abstract

Control contraction metrics (CCMs) are a new approach to nonlinear control design based on contraction theory. The resulting design problems are expressed as pointwise linear matrix inequalities and are and well-suited to solution via convex optimization. In this paper, we extend the theory on CCMs by showing that a pair of "dual" observer and controller problems can be solved using pointwise linear matrix inequalities, and that when a solution exists a separation principle holds. That is, a stabilizing output-feedback controller can be found. The procedure is demonstrated using a benchmark problem of nonlinear control: the Moore-Greitzer jet engine compressor model.