Distributed Algebraic Riccati Equations in Multi-Agent Systems

The behaviour of most modern multi-agent networked systems, used for distributed learning and control tasks, is describable by a set of interacting algebraic Riccati equations. However, due to the complexity of their behaviour, these interacting Riccati equations have, to this point, not been subject to rigorous scrutiny. To this end, a general class of algebraic Riccati equations is considered, their behaviour is analysed, and conditions for convergence to a unique set of stabilising solutions is established. The class of algebraic Riccati equations considered in this work is selected so that obtained results would be generalisable for a wide range of statistical learning and control purposes. Finally, application of the obtained results in distributed Kalman filtering and decentralised linear control is demonstrated.