On the design of multiplex control to reject disturbances in nonlinear network systems affected by heterogeneous delays

TL;DR

This paper proposes a multiplex control approach using integral control to reject polynomial disturbances in nonlinear network systems with heterogeneous delays, ensuring stability and desired behavior.

Contribution

It introduces a novel multiplex control design with integral action for nonlinear networks affected by delays and disturbances, with stability conditions derived via contraction theory.

Findings

Control protocol effectively rejects disturbances in simulations

Provides sufficient conditions for stability and performance

Demonstrates applicability on a high-voltage DC grid example

Abstract

We consider the problem of designing control protocols for nonlinear network systems affected by heterogeneous, time-varying delays and disturbances. For these networks, the goal is to reject polynomial disturbances affecting the agents and to guarantee the fulfilment of some desired network behaviour. To satisfy these requirements, we propose an integral control design implemented via a multiplex architecture. We give sufficient conditions for the desired disturbance rejection and stability properties by leveraging tools from contraction theory. We illustrate the effectiveness of the results via a numerical example that involves the control of a multi-terminal high-voltage DC grid.