Summary. 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.

Abstract. This paper addresses the problem of steering a group of vehicles along given paths while holding a desired formation pattern. The solution to this problem, henceforth referred to as the Coordinated Path-Following problem, unfolds in two basic steps. First, a path-following control law is used that drives each vehicle to its assigned path regardless of the temporal speed profile adopted. This is done by making each vehicle approach a conveniently defined virtual target that moves along the path. In the second step, the speeds of the vehicles are adjusted so as to synchronize the positions of the corresponding virtual targets (also called coordination states) thus achieving coordination along the paths. In the problem formulation, it is explicitly considered that each vehicle transmits its coordination state to only a subset of the other vehicles, as determined by the communications topology adopted. It is shown that the system that is obtained by putting together the path following and coordination strategies can be naturally viewed as a feedback interconnected system. Using this result and recent results from nonlinear system and graph theory, conditions are derived under which the path following and the coordination errors are driven to a neighborhood of zero in the presence of communication failures and time delays. Two different situations are considered. The first captures the case where the communication graph is alternately connected and disconnected (brief connectivity losses). The second reflects an operating scenario where the union of the communication graphs over uniform intervals of time remains connected (uniformly connected in mean). To better ground the paper on a non-trivial design example, a coordinated path-following algorithm is derived for multiple underactuated Autonomous Underwater Vehicles (AUVs). Simulation results are presented and discussed. Key words. Coordination control, communication losses and time delays, path-following, autonomous underwater vehicle AMS subject classifications. 1. Introduction. Increasingly

This paper introduces a mathematical model of the behavior of a group of agents and their interactions in a shared environment. We represent environmental spatial constraints that allow us to model range-limited sensing, motion, and communication capabilities of the agents. We derive general sensing, coordination, and motion conditions on the agents that guarantee that a desired distribution of the group of agents will emerge across the environment. We show the impact of group size on the distribution of agents, and consider the emergent distribution for different classes of environments. For more restrictive sensing and motion conditions we then characterize the rate at which the desired distribution is achieved. Finally, we show how this theory is useful in solving a multi-vehicle cooperative surveillance problem and discuss how our theory might be useful in understanding animal distributions in nature. I.

Decentralized connectivity maintenance in mobile networks with bounded inputs

V. CONCLUSION The technical note introduced a notion of linear i/o equivalence transformation for the set of meromorphic nonlinear higher order i/o difference equations. Then, it was proved that using the linear i/o equivalence transformations, the set of nonlinear equations can be transformed into the row-reduced form. Finally, the constructive algorithm is given for finding the equivalence transformation which extends the corresponding transformation for linear systems. The future task is to find out under which additional assumptions the concept of linear i/o equivalence coincides with the conventional i/o equivalence definition based on the i/o pairs. The problem of transforming the set of i/o difference equations into a doubly-reduced (i.e., both row- and column-reduced) form is the topic of the future paper. For that purpose the paper [5] addressing the transformation the matrix over a skew polynomial ring into a doubly-reduced form, may be helpful. Note that the doubly-reduced form is instrumental in the solution of the realization problem of the i/o difference equations into the state space form.