This paper presents an angle-based approach for distributed formation shape stabilization of multi-agent systems in the plane. We develop an angle rigidity theory to study whether a planar framework can be determined by angles between segments uniquely up to translations, rotations, scalings and reflections. The proposed angle rigidity theory is applied to the formation stabilization problem, where multiple single-integrator modeled agents cooperatively achieve an angle-constrained formation. During the formation process, the global coordinate system is unknown for each agent and wireless communications between agents are not required. Moreover, by utilizing the advantage of high degrees of freedom, we propose a distributed control law for agents to stabilize a target formation shape with desired orientation and scale. Simulation examples are performed for illustrating effectiveness of the proposed control strategies.

In this paper, the distributed Nash equilibrium (NE) searching problem is investigated, where the feasible action sets are constrained by nonlinear inequalities and linear equations. Different from most of the existing investigations on distributed NE searching problems, we consider the case where both cost functions and feasible action sets depend on actions of all players, and each player can only have access to the information of its neighbors. To address this problem, a continuous-time distributed gradient-based projected algorithm is proposed, where a leader-following consensus algorithm is employed for each player to estimate actions of others. Under mild assumptions on cost functions and graphs, it is shown that players' actions asymptotically converge to a generalized NE. Simulation examples are presented to demonstrate the effectiveness of the theoretical results.

In this paper, we study the consensus problem of discrete-time and continuous-time multiagent systems with distance-dependent communication networks, respectively. The communication weight between any two agents is assumed to be a nonincreasing function of their distance. First, we consider the networks with fixed connectivity. In this case, the interaction between adjacent agents always exists but the influence could possibly become negligible if the distance is long enough. We show that consensus can be reached under arbitrary initial states if the decay rate of the communication weight is less than a given bound. Second, we study the networks with distance-dependent connectivity. It is assumed that any two agents interact with each other if and only if their distance does not exceed a fixed range. With the validity of some conditions related to the property of the initial communication graph, we prove that consensus can be achieved asymptotically. Third, we present some applications of the main results to opinion consensus problems and formation control problems. Finally, several simulation examples are presented to illustrate the effectiveness of the theoretical findings.In this paper, we study the consensus problem of discrete-time and continuous-time multiagent systems with distance-dependent communication networks, respectively. The communication weight between any two agents is assumed to be a nonincreasing function of their distance. First, we consider the networks with fixed connectivity. In this case, the interaction between adjacent agents always exists but the influence could possibly become negligible if the distance is long enough. We show that consensus can be reached under arbitrary initial states if the decay rate of the communication weight is less than a given bound. Second, we study the networks with distance-dependent connectivity. It is assumed that any two agents interact with each other if and only if their distance does not exceed a fixed range. With the validity of some conditions related to the property of the initial communication graph, we prove that consensus can be achieved asymptotically. Third, we present some applications of the main results to opinion consensus problems and formation control problems. Finally, several simulation examples are presented to illustrate the effectiveness of the theoretical findings.

This paper considers the problem of asynchronous distributed multi-agent optimization on server-based system architecture. In this problem, each agent has a local cost, and the goal for the agents is to collectively find a minimum of their aggregate cost. A standard algorithm to solve this problem is the iterative distributed gradientdescent (DGD) method being implemented collaboratively by the server and the agents. In the synchronous setting, the algorithm proceeds from one iteration to the next only after all the agents complete their expected communication with the server. However, such synchrony can be expensive and even infeasible in realworld applications. We show that waiting for all the agents is unnecessary in many applications of distributed optimization, including distributed machine learning, due to redundancy in the cost functions (or data). Specifically, we consider a generic notion of redundancy named (r, )-redundancy implying solvability of the original multi-agent optimization problem with accuracy, despite the removal of up to r (out of total n) agents from the system. We present an asynchronous DGD algorithm where in each iteration the server only waits for (any) n − r agents, instead of all the n agents. Assuming (r, )-redundancy, we show that our asynchronous algorithm converges to an approximate solution with error that is linear in and r. Moreover, we also present a generalization of our algorithm to tolerate some Byzantine faulty agents in the system. Finally, we demonstrate the improved communication efficiency of our algorithm through experiments on MNIST and Fashion-MNIST using the benchmark neural network LeNet.Preprint. Under review.

No abstract