Consensus on Nonlinear Spaces

TL;DR: An overview of recent progress of synchronization of complex dynamical networks and its applications is presented and robustness of synchronization, controllability and observability of complex networks and synchronization of multiplex networks are focused on.

TL;DR: In this paper, a method for synthesis of distributed controllers based on linear Lyapunov functions and storage functions instead of quadratic ones was developed for analysis and design of large scale control systems.

TL;DR: Several results regarding scalable synthesis and verfication are derived, including a new stronger version of the Kalman-Yakubovich-Popov lemma for positive systems and frequency domain models using the notion of positively dominated system.

TL;DR: In this paper, a decentralized consensus control of a formation of rigid-body spacecraft is studied in the framework of geometric mechanics while accounting for a constant communication time delay between spacecraft, where relative position and attitude are represented on the Lie group SE(3) and the communication topology is modeled as a digraph.

TL;DR: A distinctive feature of this work is to address consensus problems for networks with directed information flow by establishing a direct connection between the algebraic connectivity of the network and the performance of a linear consensus protocol.

TL;DR: A theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, time-delays, and performance guarantees is provided.

TL;DR: A theoretical explanation for the observed behavior of the Vicsek model, which proves to be a graphic example of a switched linear system which is stable, but for which there does not exist a common quadratic Lyapunov function.

TL;DR: Numerical evidence is presented that this model results in a kinetic phase transition from no transport to finite net transport through spontaneous symmetry breaking of the rotational symmetry.