Decentralized Nonlinear Feedback Design with Separable Control Contraction Metrics

TL;DR

This paper presents a scalable, distributed control design method for nonlinear networks using contraction metrics, enabling exponential convergence through convex optimization.

Contribution

It introduces a constructive, convex-optimization-based approach for decentralized nonlinear feedback control using separable contraction metrics.

Findings

Successfully achieves exponential convergence in nonlinear networks

Provides a scalable, distributed control synthesis method

Demonstrates effectiveness with an illustrative example

Abstract

The problem under consideration is the synthesis of a distributed controller for a nonlinear network composed of input affine systems. The objective is to achieve exponential convergence of the solutions. To design such a feedback law, methods based on contraction theory are employed to render the controller-synthesis problem scalable and suitable to use distributed optimization. The nature of the proposed approach is constructive, because the computation of the desired feedback law is obtained by solving a convex optimization problem. An example illustrates the proposed methodology.