Robust Distributed Sub-Optimal Coordination of Linear Agents with Uncertain Input Nonlinearities

TL;DR

This paper presents a robust distributed control method for linear agents with input nonlinearities, ensuring convergence to near-optimal solutions under uncertainties using sector conditions and matrix inequalities.

Contribution

A novel control protocol for robust distributed coordination of linear agents with input nonlinearities, analyzed via a unified robust control approach.

Findings

Derived sufficient conditions for problem solvability.

Characterized conditions using matrix inequalities.

Validated effectiveness through numerical simulation.

Abstract

In this paper, we study robust distributed sub-optimal coordination of linear agents subject to input nonlinearities. Inspired by the robust agreement literature, we formulate a bounded distributed sub-optimal coordination problem, in which each agent converges to a neighborhood of the optimizer of a global optimization problem defined over a communication network. We propose a novel control protocol, and analyze convergence by employing a robust control approach, in which both the input nonlinearities and the gradients of the objective functions are treated in a unified manner via sector conditions. In particular, we derive sufficient conditions for the solvability of the considered problem and characterize them in terms of matrix inequalities. The effectiveness of the proposed method is demonstrated through a numerical simulation.