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SUMMARY We consider the multi‐agent optimization problem where multiple agents try to cooperatively optimize the sum of their local convex objective functions, subject to global inequality constraints and a convex constraint set over a network. Through characterizing the primal and dual optimal solutions as the saddle points of the associated Lagrangian function, which can be evaluated with stochastic errors, we propose the distributed primal–dual stochastic subgradient algorithms for two cases: (i) the time model is synchronous and (ii) the time model is asynchronous. In the first case, we obtain bounds on the convergence properties of the algorithm for a diminishing step size. In the second case, for a constant step size, we establish some error bounds on the algorithm's performance. In particular, we prove that the error bounds scale as nn in the number of n agents. Copyright © 2012 John Wiley & Sons, Ltd.

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Summary This paper studies the event‐triggered containment control problem for dynamical multiagent networks of general MIMO linear agents. An event‐triggered containment control strategy is provided, which consists of a control law based on a relative‐state feedback and a distributed triggering rule based on both the relative‐state information and a time‐dependent threshold function. Compared to the previous related works, our main contribution is that the triggering rule depends only on local information of communication networks. It is proved that under the proposed event‐based controller, the containment errors are uniformly ultimately bounded and the Zeno behavior can be excluded. Moreover, when the derivation constant in the threshold function is equal to zero, the containment control problem can be solved. Then, the results are extended to the event‐triggered observer‐based containment controller design.

This article addresses the distributed containment control problem in a group of agents governed by second-order dynamics with directed network topologies. Considering there are multiple leaders, we study a general second-order containment controller which can realize several different consensus modes by adjusting control gains. A necessary and sufficient condition on the control gains of the general containment controller is provided. Moreover, the delay sensitivity of the closed-loop multiagent system under the general containment controller is studied; the maximal upper bound of the constant delays is obtained. Finally, several numerical examples are used to illustrate the theoretical results.

This paper studies the consensus protocol using the information of second‐order neighbors in undirected and connected networks of linear systems with communication delays. The feedback matrix which guarantees consensus under both the proposed and the traditional protocol is given; it is shown that with this matrix, the networks under the proposed protocol converge faster than the traditional protocol. Based on this result, the delay sensitivity of the proposed protocol is considered under an assumption about the communication topology. The maximum allowable upper bound of the delays is obtained by solving certain linear matrix inequalities. Two simulation examples are presented to illustrate the effectiveness of the theoretical results.

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