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In this paper, a resilient distributed consensus algorithm is proposed based on multi-agent system to defend against the Byzantine attack. Two attack scenarios including node attack and edge attack are considered and the differences between them are described, in which the edge attack scenario is seldom considered before. The assumption for a network under g -local attacks is relaxed from (2 g + 1) -robust directed graph to (g + 1) -robust one based on a novel filtering method. The convergence and optimality are guaranteed by theoretical analysis, which ensures all the agents without attack can make an agreement and converge to a certain range. The simulation results show that for the two attack scenarios, the proposed algorithm can converge to the optimal solution of the compensation problem and the original problem, respectively. The proposed algorithm is more effective and has faster convergence speed compared with the contrast one. [ABSTRACT FROM AUTHOR]

In this paper, we address the distributed convex optimization problems for multi-agent systems. In our research, it is assumed that each agent in the multi-agent system could merely interact with its neighbors via a directed graph and is available to its own cost function. We then utilize the push-sum distributed dual averaging (PS-DDA) algorithm to tackle with the distributed optimization problem. However, we consider that there exist subgradient delays in PS-DDA algorithm. The proof of the main result which shows that the PS-DDA algorithm with subgradient delays converges and the error possesses sublinear growth of a rate O (τ 2 T − 0.5) , where T denotes the total amount of iterations, is detailed presented in this paper. Finally, a numerical example is simulated to show the performance of the algorithm we study in this paper. [ABSTRACT FROM AUTHOR]

This paper proposes two kinds of algorithms to achieve privacy-preserving consensus of multi-agent systems over undirected graphs via node decomposition mechanism and homomorphic cryptography technique. Based on the number of neighboring nodes (|Ni|), every agent is decomposed into |Ni| subagents, which are connected as a chain graph. Note that every subagent connects one and only one non-homologous subagent (generated by different agents). Information interaction between non-homologous subagents is encrypted by a homomorphic cryptography algorithm, and homologous subagents exchange information directly. In this regard, the proposed node decomposition mechanism enhances the privacy of the initial values without increasing the computational complexity of encryption. The first privacy-preserving algorithm can achieve the accurate average consensus, which means that the agreement value of every subagent is consistent with the original average consensus value. The second algorithm studies the privacy-preserving scaled consensus problem without a priori knowledge about the underlying graph. Although the final convergence values of subagents do not keep exactly the same, homologous subagents can compute the original group decision value by resorting to the product of the limit value and agent’s degree. Importantly, this algorithm also guarantees the privacy of group decision value of the whole system. Besides, it is proved that the privacy of the initial value can be preserved if the agent has at least one neutral neighbor. [ABSTRACT FROM AUTHOR]

This paper considers a nonsmooth constrained distributed convex optimization over multi-agent systems. Each agent in the multi-agent system only has access to the information of its objective function and constraint, and cooperatively minimizes the global objective function, which is composed of the sum of local objective functions. A novel continuous-time algorithm is proposed to solve the distributed optimization problem and effectively characterize the appropriate gain of the penalty function. It should be noted that the proposed algorithm is based on an adaptive strategy to avoid introducing the primal-dual variables and estimating the related exact penalty parameters. Additional, it is demonstrated that the state solution of the proposed algorithm achieves consensus and converges to an optimal solution of the optimization problem. Finally, numerical simulations are given and the proposed algorithm is applied to solve the optimal placement problem and energy consumption problem. [ABSTRACT FROM AUTHOR]

This paper proposes scalable, distributed algorithms for solving linear equations by integrating two mechanisms, termed consensus and conservation, in double-layered multiagent networks. The multiagent network considered in this paper is composed of clusters and each cluster consists of an aggregator and a subnetwork of agents. By achieving consensus and conservation through agent–agent communications in the same cluster and aggregator–aggregator communications among different clusters, respectively, distributed algorithms are devised for agents to cooperatively achieve a solution to the overall linear equation. These algorithms outperform existing algorithms, including but not limited to the following aspects—first, each agent does not have to know as much as a complete row or column of the overall equation; second, each agent only needs to control as few as two scalar states when the number of clusters and the number of agents are sufficiently large; third, the dimensions of agents’ states in the proposed algorithms do not have to be the same (while in contrast, algorithms based on the idea of standard consensus inherently require all agents’ states to be of the same dimension). Both analytical proof and simulation results are provided to validate exponential convergence of the proposed distributed algorithms in solving linear equations. [ABSTRACT FROM AUTHOR]

In this paper, we consider the predefined-time distributed optimization problems of homogeneous and heterogeneous linear multi-agent systems under undirected and connected communication topologies, in which, all agents share coupled equality constraint. In order to make all agents converge to the optimal output at predefined-time cooperatively, we propose two distributed algorithms for homogeneous and heterogeneous multi-agent systems according to time-base generator technology and output feedback, therein, the optimal output can make the global cost function reach minimum. In the design of the algorithms, the control gains are not required, which can avoid the requirement of some global information in advance. Furthermore, all agents converge to the optimal output with exponential speed, and we can set the convergence time arbitrarily. Finally, we provide examples to illustrate the effectiveness of the proposed distributed algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we consider the distributed optimization problems with linear coupling constraint of general homogeneous and heterogeneous linear multi-agent systems under weighted-balanced and strongly connected digraphs. In order to control all agents converge to the optimal output, we propose distributed control laws, therein, the optimal output can make the global cost function reach minimum. Then we guarantee the convergence of the proposed algorithms by the properties of Laplacian matrix and Lyapunov stability theorem. Furthermore, we extend the result of heterogeneous linear multi-agent system to the case that dynamics of agents are subject to external disturbances, and prove that the algorithm designed by internal model principle can make all agents reach the optimal output exactly. Finally, we provide examples to illustrate the effectiveness of the proposed distributed algorithms. [ABSTRACT FROM AUTHOR]

This paper is concerned with the private distributed optimization problem for multi-agent systems, where all agents cooperatively minimize the sum of individual convex objective functions with the additional requirement that the functions remain differential privacy. Based on the augmented Lagrangian algorithm, an effective distributed algorithm is presented to ensure the privacy by perturbing primal estimates with additive Laplace noises. The proposed algorithm is more likely to have a faster convergence rate compared to the primal-based algorithms, and has less computational burden contrast with the ADMM-based private algorithms. By means of an important factorization of weighted Laplacian matrix, it is proven that the error between optimal solution and ergodic average estimates is bounded, which is related to the privacy level. Within this framework, trade-offs between privacy level and convergence accuracy are analyzed. Finally the effectiveness of the proposed algorithm is illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of minimizing the global energy cost for multiagent systems to achieve consensus over undirected network topologies. Conventional optimization problems so defined require all-to-all network topologies for interagent communications, which precludes the use of distributed control or otherwise demands that the network be complete. To circumvent this difficulty, we introduce a network approximation (NA) scheme in the optimization criterion, which tends to render the optimization problem to one seemingly over a complete graph network, thus removing the all-to-all communication requirement. With the NA cost, we show that a distributed optimal consensus algorithm always exists for any given connected network topology, which can be determined by solving a single-agent-level parametric algebraic Ricatti equation (PARE). We also investigate the performance of the optimal consensus algorithm, focusing on the minimal energy cost required to achieve consensus optimally, and the speed at which consensus is achieved. Furthermore, for certain more special yet worthy cases, such as single-integrator, double-integrator, and first-order unstable agents, we derive explicit expressions for the energy cost and the consensus speed. It can be seen from these results that the energy cost can be made arbitrarily small for single-integrator and double-integrator systems under the optimal distributed control. On the other hand, for the first-order unstable agents, the energy cost increases and consensus speed decreases monotonically with the value of the agent's real unstable pole. [ABSTRACT FROM AUTHOR]