In this paper, we investigate a distributed estimation problem for multi-agent systems with state equality constraints (SEC). First, under a time-based consensus communication protocol, applying a modified projection operator and the covariance intersection fusion method, we propose a distributed Kalman filter with guaranteed consistency and satisfied SEC. Furthermore, we establish the relationship between consensus step, SEC and estimation error covariance in dynamic and steady processes, respectively. Employing a space decomposition method, we show that the error covariance in the constraint set can be arbitrarily small by setting a sufficiently large consensus step. Besides, we propose an extended collective observability (ECO) condition based on SEC, which is milder than existing observability conditions. Under the ECO condition, through utilizing a technique of matrix approximation, we prove the boundedness of error covariance and the exponentially asymptotic unbiasedness of state estimate, respectively. Moreover, under the ECO condition for linear time-invariant systems with SEC, we provide a novel eventtriggered communication protocol by employing the consistency, and give an offline design principle of triggering thresholds with guaranteed boundedness of error covariance. More importantly, we quantify and analyze the communication rate for the proposed event-triggered distributed Kalman filter, and provide optimization based methods to obtain the minimal (maximal) successive non-triggering (triggering) times. Two simulations are provided to demonstrate the developed theoretical results and the effectiveness of the filters

This paper investigates resource allocation problems, where the cost functions of agents are nonsmooth and the decisions of agents are constrained by heterogeneous local constraints and network resource constraints. We design a distributed subgradient-based algorithm to achieve the optimal resource allocation. Moreover, we analyze the convergence of the algorithm to the optimal solution. The algorithm can solve resource allocation problems with strongly convex cost functions and weight-balanced digraphs, as well as resource allocation problems with strictly convex cost functions and connected undirected graphs. With the algorithm, the decisions of all agents asymptotically converge to the optimal allocation. Simulation examples verify the effectiveness of the algorithm.

Learning a good initialization model from distributed data sources over multi-agent systems is highly promising, in which the tasks or data are distributed stored and not accessible to all agents. This paper focuses on the distributed meta-learning problem and proposes a distributed Reptile meta-learning algorithm. In the proposed algorithm, each agent approximates the global model through a bi-level optimization scheme, where the inner step employs a stochastic gradient descent on a specific task, and the outer step utilizes information from neighbors and a gradient-like updating. The suggested algorithm avoids calculating the Hessian-vector products during training, reducing the computational complexity and affording memory miniaturization. We further analyze the convergence properties of the proposed algorithm under the convexity assumption. Finally, we demonstrate the effectiveness of the proposed algorithm on regression and classification tasks. The results show that our algorithm approximates a centralized solution and outperforms the non-cooperative algorithm.