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This paper focuses on the distributed consensus seeking of multi-agent systems (MASs) with discrete-time control updating and intermittent communications among agents. Compared with existing linearly coupled protocols, a nonlinear coupled Zeno-free event-triggered controller is first proposed, which is further to project the static and dynamic triggering mechanisms exploited by using the deadband control method. Then, the node-based nonlinear coupled adaptive event-triggered controller with online self-tuning of time-varying coupling weight and its corresponding to static and dynamic deadband-based event-triggered mechanisms are designed, respectively. The exploited adaptive event-triggered controller does not rely on any global information of interaction structure and is implemented in a fully distributed fashion. In addition, two dynamic proposals not only cover existing static strategies as special cases, but also show that the minimal inter-execution time of dynamic one is not smaller than that of static one. Theoretical analysis shows that the proposed static and dynamic deadband-based event-triggered mechanisms can not only ensure the average consensus with Zeno-freeness, but also achieve the data reduction of communication and control. Finally, the proposed algorithms applied to circuit implementation are corroborated to prove its practical merits and validity. [ABSTRACT FROM AUTHOR]

This paper considers the constrained finite-time consensus control problem for second-order multi-agent systems with leaderless and leader–follower. By using the saturated controller design method and homogenous system theory, a finite-time consensus algorithm for multi-agent systems is proposed. Compared with the existing results, the proposed consensus algorithm makes the closed-loop system not only finite-time convergence but also satisfies the velocity constraints and input saturations. Simulation examples show the effectiveness of the proposed consensus algorithms. [ABSTRACT FROM AUTHOR]

This paper addresses the finite-time and fixed-time bipartite average tracking (BAT) problems in multi-agent systems (MASs) subject to bounded disturbances. A novel non-smooth protocol is first constructed on the basis of utilizing the finite-time control method, which can realize the finite-time BAT with structurally balanced graph. Then, the fixed-time BAT problem is dealt with nonlinear fixed-time algorithm, the setting time of which is obtained without depending on initial states. By employing Lyapunov stability theory, some sufficient criteria are obtained to achieve the finite-time and fixed-time BAT for MASs with disturbances. Numerical examples are finally developed for illustration. [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 aims at solving the bipartite containment problem for linear singular multi-agent systems (MASs) with multiple dynamic leaders over general signed digraphs, where each leader can be autonomous or dynamically evolving via interactions with its neighboring leaders. To this end, we first establish some properties for the Laplacian matrices of signed digraphs. Then, three distributed observer-based bipartite containment protocols are proposed using different local output information. Multi-step algorithms for constructing the corresponding proposed protocols are also given. It is shown that under the proposed control protocols, bipartite containment can be achieved for any admissible initial states provided that the underlying signed digraph is weakly connected. Compared to the existing related works, the major contribution of present work is that the developed results are applicable for arbitrary weakly connected signed digraphs, no matter whether they are sign-symmetric or sign-asymmetric and whether they are structurally balanced or unbalanced. Two numerical examples are finally given to demonstrate the validity of our results. [ABSTRACT FROM AUTHOR]

This paper provides a framework of designing distributed model predictive controller to reach consensus of a heterogeneous time-varying multi-agent system, and the dynamics of heterogeneous agents are modeled by double integrators and Euler-Lagrange (EL) equations. Firstly, a DMPC-based consensus algorithm is proposed, where the constraints in the algorithm depend on the heterogeneous dynamics. We prove that the resultant DMPC optimization problem is feasible with the designed controllers, which is stable when the system reaches consensus. To further reduce communication cost and solve the problem with asynchronous discrete-time information exchange, self-triggered mechanism is introduced into the framework. Trigger intervals are alternatively optimized with the control inputs, and the influence on the system performance is analyzed. Numerical examples are provided to verify the effectiveness and advantages of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This paper studies consensus problems of multi-agent systems with binary-valued communications. Different from most existing works, the agents considered in this paper can only get binary-valued observations of its neighbors’ states with random noises. A consensus algorithm is proposed: first, each agent estimates its neighbors’ states by the recursive projection algorithm; then, each agent designs the control timely based on the estimates. It is proved that the estimates of the states can converge to the true states with a faster convergence rate than that in the parameter estimation. Moreover, the states of the agents can achieve mean-square consensus, and the corresponding consensus speed can achieve $O(1/t)$ under certain conditions. Finally, simulations are given to demonstrate the theoretical results. [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, the optimal output synchronization of heterogeneous multi-agent systems is studied. To overcome the shortcoming of previous methods that require system model, a data-based optimal control policy is proposed for the output synchronization problem. Besides, the intrinsic equivalence relationship between model-based optimal solution and the proposed data-based optimal solution is proved. To solve the proposed control policy, a reinforcement learning algorithm based on measured input-output data is presented, which is different from existing model-free algorithms based on internal state. According to the algorithm, the optimal output synchronization problem of heterogeneous multi-agent systems can be solved when the full-state vector is unavailable. Finally, the effectiveness of proposed algorithm is verified by simulation examples. [ABSTRACT FROM AUTHOR]

This paper studies linear stochastic approximation (SA) algorithms and their application to multiagent systems in engineering and sociology. As main contribution, we provide necessary and sufficient conditions for convergence of linear SA algorithms to a deterministic or random final vector. We also characterize the system convergence rate, when the system is convergent. Moreover, differing from non-negative gain functions in traditional SA algorithms, this paper considers also the case when the gain functions are allowed to take arbitrary real numbers. Using our general treatment, we provide necessary and sufficient conditions to reach consensus and group consensus for first-order discrete-time multiagent system over random signed networks and with state-dependent noise. Finally, we extend our results to the setting of multidimensional linear SA algorithms and characterize the behavior of the multidimensional Friedkin–Johnsen model over random interaction networks. [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 secure state estimation problem of multiagent systems with misbehaving agents. Compared with the existing works which only consider malicious behaviors generated elaborately, a class of faulty behaviors generated randomly is also taken into account. By assuming that faulty behaviors cannot be altered by the adversaries, the notion of orthogonal complement matrix is introduced to characterize the state observability of the multiagent systems with both faulty and malicious agents. It is shown that more misbehaving agents can be tolerated by distinguishing faulty agents from malicious ones. Then, for single agent, two algorithms are provided to estimate the state based on its own value and the measurements obtained from its neighbors. Finally, two simulations are provided to illustrate the correctness and effectiveness of the proposed conditions and methods. [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]

Existing results on cooperative control of multiagent systems with unknown control directions require that the underlying topology is either fixed with a strongly connected graph or switching between different strongly connected graphs. Furthermore, in most cases the graph is assumed to be balanced. This paper proposes a new class of nonlinear proportional-integral (PI) based algorithms to relax these requirements and allow for unbalanced and switching topologies having a jointly strongly connected basis. This is made possible for single-integrator (SI) and double-integrator (DI) agents with nonidentical unknown control directions by a suitable selection of the distributed nonlinear PI functions. Moreover, as a special case, the proposed algorithms are applied to strongly connected and fixed graphs. Finally, simulation examples are given to show the validity of our theoretical results. [ABSTRACT FROM AUTHOR]

The leader-following consensus problem for linear discrete-time multiagent systems has been studied in the literature using $H_{\infty }$ Riccati inequality design and $H_{2}$ Riccati equation design methods, respectively. These two methods lead to a solvability condition in terms of an inequality that relies on a scaling gain and a fixed weighting vector called nominal weighting vector. In this paper, we further study this problem by proposing a more general class of distributed state feedback control laws, which not only depends on a scaling gain, but also a set of weighting vectors. We first establish a spectral property of a weighted graph matrix, which will be instrumental in solving the problem. Then, we present a solvability condition based on a modified algebraic Riccati equation, which is somehow more general than $H_{\infty }$ and $H_{2}$ Riccati methods, in that the solvability condition can be made satisfied by tuning the weighting vector. We show that our solvability condition is also necessary for single-input follower systems and is always satisfied for leader systems without exponentially growing modes. Moreover, in case the solvability condition is not satisfied under the nominal weighting vector, we show that our solvability condition can always be made satisfied by choosing a weighting vector other than the nominal one for multiagent systems over acyclic digraphs. [ABSTRACT FROM AUTHOR]

The circle formation problem for a group of mobile agents with limited interaction range is addressed in this paper. Distributed switching control laws are developed for multiagent systems to form prescribed formations from any initial configurations on a circle. It is shown that the desired circle formation can be achieved if a parameter depending on the agents’ interaction range is larger than the prescribed angular distance from each agent to its immediate counterclockwise agent. When the agents’ interaction range is not sufficiently large, the formation error of each agent converges to a limit, and an upper bound and a lower bound on the limit value are provided. It is also shown that under the proposed control laws, the mobile agents’ spatial order on the circle is always preserved and thus collision between mobile agents is avoided. [ABSTRACT FROM AUTHOR]

The distributed convex optimization problem is studied in this paper for any fixed and connected network with general constraints. To solve such an optimization problem, a new type of continuous-time distributed subgradient optimization algorithm is proposed based on the Karuch–Kuhn–Tucker condition. By using tools from nonsmooth analysis and set-valued function theory, it is proved that the distributed convex optimization problem is solved on a network of agents equipped with the designed algorithm. For the case that the objective function is convex but not strictly convex, it is proved that the states of the agents associated with optimal variables could converge to an optimal solution of the optimization problem. For the case that the objective function is strictly convex, it is further shown that the states of agents associated with optimal variables could converge to the unique optimal solution. Finally, some simulations are performed to illustrate the theoretical analysis. [ABSTRACT FROM AUTHOR]

Predefined mymargin finite-time output containment control problem for nonlinear multi-agent systems with multiple dynamical leaders under directed topology is investigated, where the outputs of followers can converge to the predefined convex hull formed by the multiple leaders within a finite time, and the leaders can have unknown control inputs. Firstly, for the directed topological structure among the followers, a distributed adaptive observer is designed to estimate the whole states of all the leaders under the influences of the leaders’ unknown inputs. By utilizing Hardy’s inequality and common Lyapunov theory, the finite-time convergence of the proposed observer is proved. On the basis of this conclusion, a predefined distributed containment control protocol including the desired convex combinations of the leaders is developed for each follower by using the given weights. Then an algorithm is proposed to design the control parameters in the proposed containment control protocol. With the help of the output regulation theory, the finite-time output containment criterion for nonlinear multi-agent systems in the presence of the leaders’ unknown inputs is derived. Finally, a numerical simulation example is presented to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

The PageRank algorithm employed at Google assigns a measure of importance to each web page for rankings in search results. In our recent papers, we have proposed a distributed randomized approach for this algorithm, where web pages are treated as agents computing their own PageRank by communicating with linked pages. This paper builds upon this approach to reduce the computation and communication loads for the algorithms. In particular, we develop a method to systematically aggregate the web pages into groups by exploiting the sparsity inherent in the web. For each group, an aggregated PageRank value is computed, which can then be distributed among the group members. We provide a distributed update scheme for the aggregated PageRank along with an analysis on its convergence properties. The method is especially motivated by results on singular perturbation techniques for large-scale Markov chains and multi-agent consensus. A numerical example is provided to illustrate the level of reduction in computation while keeping the error in rankings small. [ABSTRACT FROM AUTHOR]

This paper discusses consensus problems for multiagent networks under directed communication graphs. The motions of agents are described by impulsive differential equations, and thus, consensus algorithms can be designed in terms of impulsive systems. Different from the standard consensus algorithms which rely on continuous-time or discrete-time models, the proposed algorithms based on impulsive systems take advantages of instantaneous information. It is shown that the proposed algorithms have a faster convergence speed than the standard consensus algorithms. Moreover, conditions under which all agents reach consensus with the desired performance are presented for the multiagent networks with external disturbances. Simulation results demonstrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

The paper studies asynchronous consensus problems of continuous-time multi-agent systems with discontinuous information transmission. The proposed consensus control strategy is implemented based on the state information of each agent's neighbors at some discrete times. The asynchrony 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 time-dependent 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 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 the theoretical results. [ABSTRACT FROM AUTHOR]

Software systems tend to become larger and more complicated as the functional requirements increase gradually. Well-modularized software systems are widely believed to be understood, managed and evolved easily. Software module clustering problems (SMCPs) are significant and challenging problems in software engineering whose primary aim is to obtain perfect structures of software systems according to predefined rules. To solve SMCPs, it is important to design a measure which can appropriately evaluate the quality of the structures obtained. So far, the modularization quality (the basic MQ ) is widely used as the conventional measure. However, this measure does not consider global modules and edge directions between two modules. Therefore, in this paper, we design a new modularization quality measure based on the similarity, labeled as MS , to automatically guide optimization algorithms to find a good partition of software systems which considers both global modules and edge directions. To systematically validate the performance of MS , three optimization algorithms, namely hill-climbing algorithm (HC), genetic algorithm (GA), and multi-agent evolutionary algorithm (MAEA), are adopted to optimize MS on 17 real-world software systems with varying sizes. A thorough comparison shows that MS outperforms the basic MQ in guiding the optimization algorithms to find more meaningful module clusters for software systems. [ABSTRACT FROM AUTHOR]

This paper considers a cooperative tracking problem for a group of nonlinear multiagent systems under a directed graph that characterizes the interaction between the leader and the followers. All the networked systems can have different dynamics and all the dynamics are unknown. A neural network (NN) with flexible structure is used to approximate the unknown dynamics at each node. Considering that the leader is a neighbor of only a subset of the followers and the followers have only local interactions, we introduce a cooperative dynamic observer at each node to overcome the deficiency of the traditional tracking control strategies. An observer-based cooperative controller design framework is proposed with the aid of graph tools, Lyapunov-based design method, self-structuring NN, and separation principle. It is proved that each agent can follow the active leader only if the communication graph contains a spanning tree. Simulation results on networked robots are provided to show the effectiveness of the proposed control algorithms. [ABSTRACT FROM AUTHOR]

This paper concerns decentralized control of a multi-agent stochastic queueing system. The system consists of two agents, a pricing agent and a service agent. The pricing agent controls the arrival rate by dynamically setting the fee that is paid by customers who would like to receive service, while the service agent controls the rate at which customers in the system are processed. Each agent optimizes his/her own objective subject to a model which accurately specifies the component of the system that he/she is controlling but potentially mis-specifies the component that is controlled by the other agent. We are interested in optimizing the efficiency of the aggregate system when control decisions are made in this way. Decentralized agents are coordinated using transfer contracts, which define a price for occupying unit of buffer space in the system as a function of time and available capacity. Transfer contracts lead to cash transfers between agents whenever a customer enters or departs, and serve to modify each of their incentives. We characterize the contract that maximizes the efficiency of the aggregate system under decentralized control, and show that it achieves the efficiency of a centralized agent who jointly optimizes over pricing and service policies with an accurate model of the integrated system. We also show that optimal centralized efficiency is robust to mis-specification by each agent of the dynamics induced by the other in his/her model. An iterative decentralized algorithm for constructing the optimal contract and a proof of convergence is also presented. [ABSTRACT FROM AUTHOR]