Robust Output Feedback Consensus for Networked Heterogeneous Nonlinear Negative-Imaginary Systems

TL;DR

This paper develops a robust output feedback consensus protocol for heterogeneous nonlinear negative-imaginary systems, extending previous linear results to nonlinear systems and ensuring convergence despite parameter uncertainties.

Contribution

It extends the robust output feedback consensus framework from linear to nonlinear negative-imaginary systems using networked heterogeneous controllers.

Findings

Proves the network of nonlinear NI systems remains NI.

Shows the network of nonlinear OSNI controllers is also OSNI.

Demonstrates convergence of all outputs to a common trajectory despite parameter perturbations.

Abstract

This paper provides a control protocol for the robust output feedback consensus of networked heterogeneous nonlinear negative-imaginary (NI) systems. Heterogeneous nonlinear output strictly negative-imaginary (OSNI) controllers are applied in positive feedback according to the network topology to achieve output feedback consensus. The main contribution of this paper is extending the previous studies of the robust output feedback consensus problem for networked heterogeneous linear NI systems to nonlinear NI systems. Output feedback consensus is proved by investigating the internal stability of the closed-loop interconnection of the network of heterogeneous nonlinear NI plants and the network of heterogeneous nonlinear OSNI controllers according to the network topology. The network of heterogeneous nonlinear NI systems is proved to be also a nonlinear NI system, and the network of heterogeneous nonlinear OSNI systems is proved to be also a nonlinear OSNI system. Under suitable conditions, the nonlinear OSNI controllers lead to the convergence of the outputs of all nonlinear NI plants to a common limit trajectory, regardless of the system model of each plant. Hence, the protocol is robust with respect to parameter perturbation in the system models of the heterogeneous nonlinear NI plants in the network.