The interrelationship between control and communication theory is becoming of fundamental importance in many distributed control systems, such as the coordination of a team of autonomous agents. In such a problem, communication constraints impose limits on the achievable control performance. We consider as instance of coordination the consensus problem. The aim of the paper is to characterize the relationship between the amount of information exchanged by the agents and the rate of convergence to the consensus. We show that time-invariant communication networks with circulant symmetries yield slow convergence if the amount of information exchanged by the agents does not scale well with their number. On the other hand, we show that randomly time-varying communication networks allow very fast convergence rates. We also show that, by adding logarithmic quantized data links to time-invariant networks with symmetries, control performance significantly improves with little growth of the required communication effort.

The interrelationship between control and communication theory is becoming of fundamental importance in many distributed control systems. Particular examples are systems comprised of multiple agents. When it comes to coordinately control a group of autonomous mobile agents in order to achieve a common task, communication constraints impose limits on the achievable control performance. In this paper we consider a widely studied problem in the robotics and control communities, called consensus or state agreement problem. The aim of the paper is to characterize the relationship between the amount of information exchanged by the agents and the rate of convergence to the agreement. Time-invariant communication networks that exhibit particular symmetries are shown to yield slow convergence if the amount of information exchanged does not scale with the number of agents. On the other hand, we show that, randomly time-varying communication networks allow very fast convergence rates. The last part of the paper is devoted to the study of time-invariant communication networks with logarithmic quantized data exchange among the agents. It is shown that, by adding quantized data links to the network, the control performance significantly improves with little growth of the required communication effort.

In a sensor network, in practice, the communication among sensors is subject to: (1) errors or failures at random times; (2) costs; and (3) constraints since sensors and networks operate under scarce resources, such as power, data rate, or communication. The signal-to-noise ratio (SNR) is usually a main factor in determining the probability of error (or of communication failure) in a link. These probabilities are then a proxy for the SNR under which the links operate. The paper studies the problem of designing the topology, i.e., assigning the probabilities of reliable communication among sensors (or of link failures) to maximize the rate of convergence of average consensus, when the link communication costs are taken into account, and there is an overall communication budget constraint. To consider this problem, we address a number of preliminary issues: (1) model the network as a random topology; (2) establish necessary and sufficient conditions for mean square sense (mss) and almost sure (a.s.) convergence of average consensus when network links fail; and, in particular, (3) show that a necessary and sufficient condition for both mss and a.s. convergence is for the algebraic connectivity of the mean graph describing the network topology to be strictly positive. With these results, we formulate topology design, subject to random link failures and to a communication cost constraint, as a constrained convex optimization problem to which we apply semidefinite programming techniques. We show by an extensive numerical study that the optimal design improves significantly the convergence speed of the consensus algorithm and can achieve the asymptotic performance of a non-random network at a fraction of the communication cost.

Several consensus protocols have been proposed in the literature and their convergence properties studied via a variety of methods. In all these methods, the communication topologies play a key role in the convergence of consensus processes. The goal of this paper is two fold. First, we explore communication topologies, as implied by the communication assumptions, that lead to consensus among agents. For this, several important results in the literature are examined and the focus is on different classes of communication assumptions being made, such as synchronism, connectivity, and direction of communication. In the latter part of this paper, we show that the confluent iteration graph unifies various communication assumptions and proves to be fundamental in understanding the convergence of consensus processes. In particular, based on asynchronous iteration methods for nonlinear paracontractions, we establish a new result which shows that consensus is reachable under directional, time-varying and asynchronous topologies with nonlinear protocols. This result extends the existing ones in the literature and have many potential applications. 1

Abstract — We consider stochastic consensus problems in strongly connected directed graph models where each agent has noisy measurements of its neighbors ’ states. For consensus seeking, we develop stochastic approximation type algorithms with a decreasing step size and establish mean square and almost sure convergence of the agents ’ states to the same limit. I.

We consider a formation control system where individual systems are controlled by a path-following design and the path variables are to be synchronized. We first show a passivity property for the path following system and, next, combine this with a passivity-based synchronization algorithm developed in [1]. The passivity approach expands the classes of synchronization schemes available to the designer. This generality offers the possibility to optimize controllers to, e.g., improve robustness and performance. Two designs are developed in the proposed passivity framework: The first employs the path error information in the synchronization loop, while the second only uses synchronization errors. A sampled-data design, where the path variables are updated in discrete-time and the path following controllers are updated in continuous time, is also developed.

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We propose a novel agreement framework for multiple (possibly heterogeneous) agents evolving on a directed information graph with non-uniform delays. Our proposed framework can ensure agreement of a certain scalar quantity among the agents, as long as 1) for each agent, we can design a local control s.t. its closed-loop transfer function has unit gain at dc and gain strictly less than unity elsewhere; 2) the information graph has a globally reachable node (i.e. there exists a path from it to every other nodes); and 3) the information delays are finite constants. Rendezvous simulation is performed to verify the theory.

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In this paper, we study asynchronous consensus problems of continuous-time multiagent systems with discontinuous information transmission. The proposed consensus control strategy is implemented only based on the state information at some discrete times of each agent’s neighbors. The asynchronization means that each agent’s update times, at which the agent adjusts its dynamics, are independent of others’. Furthermore, it is assumed that the communication topology among agents is timedependent and the information transmission is with bounded time-varying delays. If the union of the communication topology across any time interval with some given length contains a spanning tree, the consensus problem is shown to be solvable. The analysis tool developed in this paper is based on the nonnegative matrix theory and graph theory. The main contribution of this paper is to provide a valid distributed consensus algorithm that overcomes the difficulties caused by unreliable communication channels, such as intermittent information transmission, switching communication topology, and time-varying communication delays, and therefore has its obvious practical applications. Simulation examples are provided to demonstrate the effectiveness of our theoretical results. Key words: Multi-agent systems, asynchronous consensus, switching topology, time-varying delays, coordination. PACS: