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)

Pull-Based Distributed Event-triggered Consensus for Multi-agent Systems with Directed Topologies

This paper mainly investigates consensus problem with pull-based event-triggered feedback control. For each agent, the diffusion coupling feedbacks are based on the states of its in-neighbors at its latest triggering time and the next triggering time of this agent is determined by its in-neighbors' information as well. The general directed topologies, including irreducible and reducible cases, are investigated. The scenario of distributed continuous monitoring is considered firstly, namely each agent can observe its in-neighbors' continuous states. It is proved that if the network topology has a spanning tree, then the event-triggered coupling strategy can realize consensus for the multi-agent system. Then the results are extended to discontinuous monitoring, i.e., self-triggered control, where each agent computes its next triggering time in advance without having to observe the system's states continuously. The effectiveness of the theoretical results are illustrated by a numerical example finally.Comment: arXiv admin note: text overlap with arXiv:1407.137

Steering opinion dynamics via containment control

In this paper, we model the problem of influencing the opinions of groups of individuals as a containment control problem, as in many practical scenarios, the control goal is not full consensus among all the individual opinions, but rather their containment in a certain range, determined by a set of leaders. As in classical bounded confidence models, we consider individuals affected by the confirmation bias, thus tending to influence and to be influenced only if their opinions are sufficiently close. However, here we assume that the confidence level, modeled as a proximity threshold, is not constant and uniform across the individuals, as it depends on their opinions. Specifically, in an extremist society, the most radical agents (i.e., those with the most extreme opinions) have a higher appeal and are capable of influencing nodes with very diverse opinions. The opposite happens in a moderate society, where the more connected (i.e., influential) nodes are those with an average opinion. In three artificial societies, characterized by different levels of extremism, we test through extensive simulations the effectiveness of three alternative containment strategies, where leaders have to select the set of followers they try to directly influence. We found that, when the network size is small, a stochastic time-varying pinning strategy that does not rely on information on the network topology proves to be more effective than static strategies where this information is leveraged, while the opposite happens for large networks where the relevance of the topological information is prevalent

Event-triggered pinning control of switching networks

This paper investigates event-triggered pinning control for the synchronization of complex networks of nonlinear dynamical systems. We consider networks described by time-varying weighted graphs and featuring generic linear interaction protocols. Sufficient conditions for the absence of Zeno behavior are derived and exponential convergence of a global normed error function is proven. Static networks are considered as a special case, wherein the existence of a lower bound for interevent times is also proven. Numerical examples demonstrate the effectiveness of the proposed control strategy

Nodes selection strategy in cooperative tracking problem

In this paper, a new optimization problem is addressed for node selection that has application potentials in input/output switches for sensors in control system design and leader determination in social networks. The purpose of the addressed problem is to develop a strategy for selecting a subset of nodes as controlled nodes in order to minimize certain objective function consisting of the convergence speed and the energy of control action, over a finite time-horizon. For networks with fixed controlled nodes, an upper bound of the objective function is obtained which is shown to be convex and independent of the time-horizon. For networks with switched controlled nodes, a greedy algorithm is proposed to reduce the computation complexity resulting from the length of the time-horizon, where the nodes selection is carried out over divided small time-intervals. The cost gap is also analyzed between the strategy of optimizing over the whole time-horizon and the strategy of optimizing over the small intervals. Finally, the proposed nodes selection strategy is validated through simulations and two regions are found in which the number of optimal controlled nodes is determined