This paper studies the differentially private consensus problem of multiagent networks by employing a distributed event-triggered mechanism such that not only agents can protect the privacy of their initial states from information disclosure, but the execution efficiency of the whole network can be improved. First, we propose a distributed event-triggered mechanism for a differentially private consensus algorithm such that frequent real-time communication and controller updates can be avoided. Second, we propose a distributed event-triggering condition that only depends on local information and local parameters, which can effectively avoid global information collection. Third, the convergence analysis of the mean-square average consensus is given to explain the sufficiency of the proposed event-triggered mechanism and event-triggering condition. Furthermore, we establish the statistic properties of the convergent accuracy that the expectation of the convergence point converges to the average value of all agents' initial states exactly and the disturbance variance is bounded with an explicit expression. In addition, we further give the differential privacy analysis that each agent can flexibly select its own privacy level to prevent information disclosure. Finally, simulation results are given to illustrate the effectiveness of the proposed mechanism and the correctness of the theoretical results.

This paper is concerned with a communication-efficient algorithm update scheme for solving distributed convex optimization problems by introducing a distributed event-triggered approach. Compared with real-time consensus-based distributed optimization algorithms in the literature, this paper focuses on extending the real-time gradient tracking scheme and proposes a novel distributed event-triggering condition to reduce the frequency of information exchange between agents in a network. The proposed event-triggered approach for consensus-based distributed optimization algorithms not only avoids the real-time consecutive communication and the coordinated computation between agents but reduces the computation load of algorithm execution. Furthermore, the proposed event-triggering condition depends on only local states from neighbors at only their event times and does not require a global and homogeneous sampling period. In addition, this paper analytically shows that the proposed consensus-based distributed optimization algorithm based on an event-triggered approach can also converge to the exact optimal solution with a linear convergence rate even if the real-time consecutive communication between agents is replaced with sporadic communication.

This paper is concerned with the study of robust distributed average tracking (DAT) algorithms for networked control systems in the presence of external disturbances or false data injection attacks (FDIAs). To eliminate the impacts of external disturbances and FDIAs, the technologies of disturbance-observer-based control (DOBC) and active disturbance rejection control (ADRC) are introduced into the context of DAT problems. First, for a class of external disturbances with known dynamics, we propose an anti-disturbance DAT (AD-DAT) algorithm, where a stand-alone disturbance observer based on the idea of DOBC is employed to estimate the disturbance and then to compensate it in the design of control inputs. The proposed AD-DAT algorithm can track the average of multiple time-varying reference signals with zero steady-state error and the accurate tracking is robust with respect to initialization constraints. Furthermore, for another class of FDIAs with unknown dynamics, we design an anti-attack DAT (AA-DAT) algorithm where the control input is based on the estimates of states instead of original states, and construct an extended state observer including a state observer and an FDIAs observer based on the idea of ADRC. The extended state observer plays a key role in estimating and eliminating the impact of FDIAs without compromising the accurate tracking performance. In addition, sufficient conditions are derived for the proposed two algorithms from a theoretical point of view to guarantee accurate average tracking. Finally, some numerical examples are given to illustrate the validity and effectiveness of the proposed algorithms. Note to Practitioners —This paper is motivated by the problem of robust distributed average tracking (DAT) for the time-varying centroid of the formation of a group of autonomous vehicles. The problem arises in the scenario where two groups of unmanned ground vehicles (UGVs) and unmanned aerial vehicles (UAVs) perform a combined surveillance-reconnaissance mission (where the UAVs aim to provide aerial coverage and early warning against threats for the UGVs, as shown in Fig. 1) in an uncertain environment where the external disturbances might exist or the FDIAs might be launched by adversaries. Obviously, the tracking accuracy of the target signal will be compromised in the presence of external disturbances or FDIAs. However, most existing works for disturbance rejection mainly focused on the static average consensus rather than the dynamic one even though a few works mentioned the DAT problem with only considering the case of external disturbances. Based on this, we propose an AD-DAT algorithm and an AA-DAT algorithm for the DAT problem based on the ideas of DOBC and ADRC, respectively. Numerical examples show that the proposed algorithms are able to estimate and eliminate the impacts of the external disturbances and the FDIAs, which implies that the algorithms can be implemented in practical scenarios. In future research, we will extend the results to more general scenarios in the presence of external disturbances and FDIAs.

This brief focuses on the dynamic weighted average consensus problem and aims to achieve accurate tracking of the weighted average of all the time-varying reference signals in a network. We first propose a robust dynamic weighted average consensus (RDWAC) algorithm that employs a simple fixed control gain and introduces an individual weight for each agent compared with recent works. Furthermore, a theoretical finite-time convergence analysis instead of an asymptotic one is provided by constructing a novel Lyapunov function, which shows that the accurate weighted average consensus can be reached exponentially within a finite time interval. In addition, the lower bound of the required convergence time is given and the relationship between the lower bound and the initial steady-state error and control parameters is established explicitly. Finally, some numerical examples are given to illustrate the effectiveness of the proposed algorithm.

This article considers distributed optimization by a group of agents over an undirected network. The objective is to minimize the sum of a twice differentiable convex function and two possibly nonsmooth convex functions, one of which is composed of a bounded linear operator. A novel distributed primal-dual fixed point algorithm is proposed based on an adapted metric method, which exploits the second-order information of the differentiable convex function. Furthermore, by incorporating a randomized coordinate activation mechanism, we propose a randomized asynchronous iterative distributed algorithm that allows each agent to randomly and independently decide whether to perform an update or remain unchanged at each iteration, and thus alleviates the communication cost. Moreover, the proposed algorithms adopt nonidentical stepsizes to endow each agent with more independence. Numerical simulation results substantiate the feasibility of the proposed algorithms and the correctness of the theoretical results.