Optimal Design for Synchronization of Cooperative Systems: State Feedback, Observer and Output Feedback

TLDR

The study considers a leader node generating a desired tracking trajectory and extends classical duality concepts to networked systems. The note investigates synchronization of identical linear systems on digraphs with a spanning tree and proposes a cooperative tracking control framework. The framework employs full state feedback, observer design, and dynamic output‑feedback control at each node. Unbounded synchronization regions are guaranteed on any digraph with a spanning tree using LQR‑based optimal control and observer design at each node.

Abstract

This technical note studies synchronization of identical general linear systems on a digraph containing a spanning tree. A leader node or command generator is considered, which generates the desired tracking trajectory. A framework for cooperative tracking control is proposed, including full state feedback control, observer design and dynamic output feedback control. The classical system theory notion of duality is extended to networked systems. It is shown that unbounded synchronization regions that achieve synchronization on arbitrary digraphs containing a spanning tree can be guaranteed by using linear quadratic regulator based optimal control and observer design methods at each node.