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This paper provides a solution for the preservation of consensus in a network of several agents, described by discrete-time nonlinear dynamical systems. Consensus preservation is the problem of maintaining a certain distance between the states of several systems, given that the systems' initial states are close to each other. The agents are equipped with both a smart sensor, capable of measuring the state of the system and performing some computations, and a controller. The sensors and controllers are placed at locations that are remote from one another. A network of communication channels with limited transmission capacity connects the agents by allowing the sensors to send messages to the controllers of their system as well as to the controllers of other systems. The controllers use the messages that they receive to steer the agents such that the consensus is preserved. Sensors and controllers that achieve this feature are called consensus-preserving protocols. In this paper, three distinct consensus-preserving protocols are presented, each with an increasing degree of interaction between the systems. For each of these protocols, a theorem providing conditions on the minimum communication capacity sufficient to implement them is presented. The protocols are tested by simulations for a network of logistic maps and a network of Hénon maps. For both of these networks, analytical bounds on the sufficient transmission capacities in the communication channels to implement the protocols are provided. These bounds are compared to rates observed in simulations of the consensus-preserving protocols. [ABSTRACT FROM AUTHOR]

When synchronization sets in, coupled systems oscillate in a coherent way. It is possible to observe also some intermediate regimes characterized by incomplete synchrony which are referred to as partial synchronization. The paper focuses on analysis of partial synchronization in networks of linearly coupled oscillators. [ABSTRACT FROM AUTHOR]

Synchronization in identical drive-response systems is a problem that can be cast in an observer design framework. In this paper we extend this approach by studying the analysis/design of partial synchronization by means of observer theory. In doing so, we introduce the concept of partial observer—an observer to reconstruct a part of the system state vector. It is also shown how the observability condition can be utilized to analyze the dynamics in an array of coupled identical systems. [ABSTRACT FROM AUTHOR]

In this Letter we analyze the concept of partial synchronization as observer design. Our aim is to estimate a signal, the function of the coordinates of a particular system that, when considering a specific output, is not necessarily fully observable. [ABSTRACT FROM AUTHOR]

Examines the problems of synchronization and control of chaotic systems. Application of the speed-gradient method in solving problems for continuous-time systems; Master-slave synchronization; Duffing's system.

This erratum corrects a mistake previously published by the author [A. Y. Pogromsky, Chaos 18, 037107 (2008)]. [ABSTRACT FROM AUTHOR]