Consensus analysis of multiagent networks via aggregated and pinning approaches

This is the post-print version of of the Article - Copyright @ 2011 IEEEIn this paper, the consensus problem of multiagent nonlinear directed networks (MNDNs) is discussed in the case that a MNDN does not have a spanning tree to reach the consensus of all nodes. By using the Lie algebra theory, a linear node-and-node pinning method is proposed to achieve a consensus of a MNDN for all nonlinear functions satisfying a given set of conditions. Based on some optimal algorithms, large-size networks are aggregated to small-size ones. Then, by applying the principle minor theory to the small-size networks, a sufficient condition is given to reduce the number of controlled nodes. Finally, simulation results are given to illustrate the effectiveness of the developed criteria.This work was jointly supported by CityU under a research grant (7002355) and GRF funding (CityU 101109)

Optimal Network Topology for Effective Collective Response

Natural, social, and artificial multi-agent systems usually operate in dynamic environments, where the ability to respond to changing circumstances is a crucial feature. An effective collective response requires suitable information transfer among agents, and thus is critically dependent on the agents' interaction network. In order to investigate the influence of the network topology on collective response, we consider an archetypal model of distributed decision-making---the leader-follower linear consensus---and study the collective capacity of the system to follow a dynamic driving signal (the "leader") for a range of topologies and system sizes. The analysis reveals a nontrivial relationship between optimal topology and frequency of the driving signal. Interestingly, the response is optimal when each individual interacts with a certain number of agents which decreases monotonically with the frequency and, for large enough systems, is independent of the size of the system. This phenomenology is investigated in experiments of collective motion using a swarm of land robots. The emergent collective response to both a slow- and a fast-changing leader is measured and analyzed for a range of interaction topologies. These results have far-reaching practical implications for the design and understanding of distributed systems, since they highlight that a dynamic rewiring of the interaction network is paramount to the effective collective operations of multi-agent systems at different time-scales

Protocol selection for second-order consensus against disturbance

Noticing that both the absolute and relative velocity protocols can solve the second-order consensus of multi-agent systems, this paper aims to investigate which of the above two protocols has better anti-disturbance capability, in which the anti-disturbance capability is measured by the L2 gain from the disturbance to the consensus error. More specifically, by the orthogonal transformation technique, the analytic expression of the L2 gain of the second-order multi-agent system with absolute velocity protocol is firstly derived, followed by the counterpart with relative velocity protocol. It is shown that both the L2 gains for absolute and relative velocity protocols are determined only by the minimum non-zero eigenvalue of Laplacian matrix and the tunable gains of the state and velocity. Then, we establish the graph conditions to tell which protocol has better anti-disturbance capability. Moreover, we propose a two-step scheme to improve the anti-disturbance capability of second-order multi-agent systems. Finally, simulations are given to illustrate the effectiveness of our findings

Dynamic Resilient Containment Control in Multirobot Systems

In this article, we study the dynamic resilient containment control problem for continuous-time multirobot systems (MRSs), i.e., the problem of designing a local interaction protocol that drives a set of robots, namely the followers, toward a region delimited by the positions of another set of robots, namely the leaders, under the presence of adversarial robots in the network. In our setting, all robots are anonymous, i.e., they do not recognize the identity or class of other robots. We consider as adversarial all those robots that intentionally or accidentally try to disrupt the objective of the MRS, e.g., robots that are being hijacked by a cyber–physical attack or have experienced a fault. Under specific topological conditions defined by the notion of (r,s)-robustness, our control strategy is proven to be successful in driving the followers toward the target region, namely a hypercube, in finite time. It is also proven that the followers cannot escape the moving containment area despite the persistent influence of anonymous adversarial robots. Numerical results with a team of 44 robots are provided to corroborate the theoretical findings