Abstract-In this paper, we discuss consensus problems for networks of dynamic agents with fixed and switching topologies. We analyze three cases: 1) directed networks with fixed topology; 2) directed networks with switching topology; and 3) undirected networks with communication time-delays and fixed topology. We introduce two consensus protocols for networks with and without time-delays and provide a convergence analysis in all three cases. We establish a direct connection between the algebraic connectivity (or Fiedler eigenvalue) of the network and the performance (or negotiation speed) of a linear consensus protocol. This required the generalization of the notion of algebraic connectivity of undirected graphs to digraphs. It turns out that balanced digraphs play a key role in addressing average-consensus problems. We introduce disagreement functions for convergence analysis of consensus protocols. A disagreement function is a Lyapunov function for the disagreement network dynamics. We proposed a simple disagreement function that is a common Lyapunov function for the disagreement dynamics of a directed network with switching topology. A distinctive feature of this work is to address consensus problems for networks with directed information flow. We provide analytical tools that rely on algebraic graph theory, matrix theory, and control theory. Simulations are provided that demonstrate the effectiveness of our theoretical results.

This paper provides 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. An overview of basic concepts of information consensus in networks and methods of convergence and performance analysis for the algorithms are provided. Our analysis framework is based on tools from matrix theory, algebraic graph theory, and control theory. We discuss the connections between consensus problems in networked dynamic systems and diverse applications including synchronization of coupled oscillators, flocking, formation control, fast consensus in small-world networks, Markov processes and gossip-based algorithms, load balancing in networks, rendezvous in space, distributed sensor fusion in sensor networks, and belief propagation. We establish direct connections between spectral and structural properties of complex networks and the speed of information diffusion of consensus algorithms. A brief introduction is provided on networked systems with nonlocal information flow that are considerably faster than distributed systems with latticetype nearest neighbor interactions. Simulation results are presented that demonstrate the role of small-world effects on the speed of consensus algorithms and cooperative control of multi-vehicle formations.

In this paper, we present a theoretical framework for design and analysis of distributed flocking algorithms. Two cases of flocking in free-space and presence of multiple obstacles are considered. We present three flocking algorithms: two for free-flocking and one for constrained flocking. A comprehensive analysis of the first two algorithms is provided. We demonstrate the first algorithm embodies all three rules of Reynolds. This is a formal approach to extraction of interaction rules that lead to the emergence of collective behavior. We show that the first algorithm generically leads to regular fragmentation, whereas the second and third algorithms both lead to flocking. A systematic method is provided for construction of cost functions (or collective potentials) for flocking. These collective potentials penalize deviation from a class of lattice-shape objects called α-lattices. We use a multi-species framework for construction of collective potentials that consist of flock-members, or α-agents, and virtual agents associated with α-agents called β-and γ-agents. We show that the tracking/migration problem for flocks can be solved using an algorithm with a peer-to-peer architecture. Each node (or macro-agent) of this peer-to-peer network is the aggregation of all three species of agents. The implication of this fact is that "flocks need no leaders". We discuss what constitutes flocking and provide a universal definition of "flocking" for particle systems that has the same role as "Lyapunov stability" for nonlinear dynamical systems. By "universal", we mean independent of the method of trajectory generation for particles. Various simulation results are provided that demonstrate the effectiveness of our novel algorithms and analytical tools. This includes performing 2-D and 3-D flocking, split/rejoin maneuver, and squeezing maneuver for 40 to 150 agents (e.g. particles and UAVs).

In this paper, we introduce three novel distributed Kalman filtering (DKF) algorithms for sensor networks. The first algorithm is a modification of a previous DKF algorithm presented by the author in CDC-ECC '05. The previous algorithm was only applicable to sensors with identical observation matrices which meant the process had to be observable by every sensor. The modified DKF algorithm uses two identical consensus filters for fusion of the sensor data and covariance information and is applicable to sensor networks with different observation matrices. This enables the sensor network to act as a collective observer for the processes occurring in an environment. Then, we introduce a continuous-time distributed Kalman filter that uses local aggregation of the sensor data but attempts to reach a consensus on estimates with other nodes in the network. This peer-to-peer distributed estimation method gives rise to two iterative distributed Kalman filtering algorithms with different consensus strategies on estimates. Communication complexity and packet-loss issues are discussed. The performance and effectiveness of these distributed Kalman filtering algorithms are compared and demonstrated on a target tracking task.

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