Network Connectivity Assumptions Research Articles

Leader selection in networks under switching topologies with antagonistic interactions

In leader–follower networks, leader selection is an important issue, and efficient schemes of selecting a group of leaders are sought to guarantee the desired coordination performance. In this paper, we study the leader selection problem under switching topologies, and aim to minimize the number of leaders to ensure the consensus of high-order multiagent systems with antagonistic interactions, which are usually represented by negative edge weights on a communication graph. First, as the basis of leader selection, sufficient conditions including average dwell time bounds for each possible topology and a mild network connectivity assumption are derived for followers to reach the expected property. Second, by applying the derived consensus criterion, metrics for identifying leaders are established via the submodular optimization method, and the supermodularity of the metrics is proved in the digraph case. Third, by utilizing the established metrics, a leader selection scheme with two polynomial-time algorithms is presented to determine leaders dynamically, and the optimality of the returned solution has a provable guarantee. Finally, the performance of the proposed leader selection scheme is demonstrated by numerical examples.

Distributed State Estimation Using Intermittently Connected Robot Networks

This paper considers the problem of distributed state estimation using multi-robot systems. The robots have limited communication capabilities and, therefore, communicate their measurements intermittently only when they are physically close to each other. To decrease the distance that the robots need to travel only to communicate, we divide them into small teams that can communicate at different locations to share information and update their beliefs. Then, we propose a new distributed scheme that combines (i) communication schedules that ensure that the network is intermittently connected, and (ii) sampling-based motion planning for the robots in every team with the objective to collect optimal measurements and decide a location for those robots to communicate. To the best of our knowledge, this is the first distributed state estimation framework that relaxes all network connectivity assumptions, and controls intermittent communication events so that the estimation uncertainty is minimized. We present simulation results that demonstrate significant improvement in estimation accuracy compared to methods that maintain an end-to-end connected network for all time.

Distributed Consensus Control of Multi-agent Systems with Higher Order Agent Dynamics and Dynamically Changing Directed Interaction Topologies

In 2005, Ren and Beard, under the network connectivity assumption that the union of the directed interaction graphs contains a spanning tree frequently enough, proposed a control protocol to solve the distributed consensus control problem for a multi-agent system with first order integrator agent dynamics. The consensus control protocol for second order systems proposed by the same authors, Ren and Beard, requires that the switching directed interaction graph has a spanning tree at every time instant to guarantee consensus. In this technical note, we propose a distributed consensus control protocol which extends the first order system results of Ren and Beard to agents represented by a general higher order controllable linear system, under the same network connectivity assumption that the union of the directed interaction graphs contains a spanning tree frequently enough. We show that the consensus can be achieved asymptotically by the group of agents under our proposed distributed control protocol. Simulation study illustrates the effectiveness of our proposed method.

Synchronization of coupled harmonic oscillators in a dynamic proximity network

In this paper, we revisit the synchronization problems for coupled harmonic oscillators in a dynamic proximity network. Unlike many existing algorithms for distributed control of complex dynamical networks that require explicit assumptions on the network connectivity, we show that the coupled harmonic oscillators can always be synchronized, without imposing any network connectivity assumption. Moreover, we also investigate the synchronization with a leader and show that all harmonic oscillators can asymptotically attain the position and velocity of the leader, again without any assumption on connectivity of the followers. Numerical simulation illustrates the theoretical results.