Distributed Robust Control of Linear Multi-Agent Systems with Parameter Uncertainties

TL;DR

This paper develops distributed robust control strategies for uncertain linear multi-agent systems with undirected communication, providing new algorithms and conditions for both continuous- and discrete-time cases to ensure quadratic stability and disturbance rejection.

Contribution

It introduces a two-step, conservative-free algorithm for continuous-time systems and LMI-based conditions for discrete-time systems, advancing robust control design for heterogeneous multi-agent systems.

Findings

Distributed controllers achieve quadratic stability under uncertainties.

The algorithms decouple feedback gain design from communication topology.

Conditions for controller existence are derived via linear matrix inequalities.

Abstract

This paper considers the distributed robust control problems of uncertain linear multi-agent systems with undirected communication topologies. It is assumed that the agents have identical nominal dynamics while subject to different norm-bounded parameter uncertainties, leading to weakly heterogeneous multi-agent systems. Distributed controllers are designed for both continuous- and discrete-time multi-agent systems, based on the relative states of neighboring agents and a subset of absolute states of the agents. It is shown for both the continuous- and discrete-time cases that the distributed robust control problems under such controllers in the sense of quadratic stability are equivalent to the $H_\infty$ control problems of a set of decoupled linear systems having the same dimensions as a single agent. A two-step algorithm is presented to construct the distributed controller for the continuous-time case, which does not involve any conservatism and meanwhile decouples the feedback gain design from the communication topology. Furthermore, a sufficient existence condition in terms of linear matrix inequalities is derived for the distributed discrete-time controller. Finally, the distributed robust $H_\infty$ control problems of uncertain linear multi-agent systems subject to external disturbances are discussed.