Ultrafast consensus via predictive mechanisms

Abstract

-An important natural phenomenon surfaces that ultrafast consensus can be achieved by introducing predictive mechanisms. By predicting the dynamics of a network several steps ahead and using this information in the consensus protocol, it is shown that, without changing the topology of the network, drastic improvements can be achieved in terms of the speed of convergence towards consensus and of the feasible range of sampling periods, compared with the routine consensus protocol. In natural science, this study provides an evidence for the idea that some predictive mechanisms exist in widely-spread biological swarms, flocks, and schools. From the industrial engineering point of view, inclusion of an efficient predictive mechanism allows for a significant increase in the consensus speed and a reduction of the required communication energy. . The collective dynamics of networks of interconnected agents is currently a subject of intensive research that has potential applications in biology, physics and engineering. In this area, one of the most general and attractive topic is the consensus problem [6][7][8], where groups of agents agree upon certain quantities such as attitude, position, temperature and voltage. Furthermore, solving consensus problem using distributed computational methods has direct implications on sensor network data fusion, load balancing, swarm control, unmanned air vehicles (UAVs), attitude alignment of satellite clusters, congestion control of communication networks, multi-agent formation control, etc. [9][10][11].One of the central problems in the study of collective dynamics is the design of consensus protocols allowing to reach consensus as quickly as possible using the least amount of communication energy. Recently, by using parallel and distributed computing approaches [12] or (a) E-mail: mc274@le.ac.uk numerical statistical analysis, some methods aiming at enhancing the consensus speed have been proposed, such as convex optimization [13], introduction of long-range interactions [14], stability analysis [15], the relation between communication intensity and convergence speed [16], design of the heterogeneous influences [17], and use of adaptive velocity [18]. Most of the previous studies on the consensus of interconnected agents has been based on the implicit assumption that an agent's state at the next discrete-time step is solely determined by the current (network) state. However, in natural bio-groups, individuals typically have some higher-level intelligence, namely predictive intelligence, which is the ability of predicting the future position of some group members based on their past and current positions. Microscopically, recent experiments on the bio-eyesight systems have revealed the predictive functions of the optical and acoustical apparatuses, especially the retina and cortex [19][20][21]. Macroscopically, experiments on bee groups [22,23] have provided evidences for the existence of predictive mechanisms in bee swarm formation and foraging. Unfortunately, predictive m...

Accelerating consensus of self-driven swarm via adaptive speed

“…For example, the swarm of fish and birds can always hold consensus under the varying of the direction and speed of the leader's motion, which can not be well explained by traditional models with local interactions since such systems require very long convergence time suffered by the change of leader's direction. A recent work [18,19] highlighted the predictive intelligence embedded in organisms, by which collectively moving agents achieve the consensus within a very short time period. Therefore, it is expected that the predictive intelligence actually plays a crucial role in a real biological swarm.…”

Improve consensus via decentralized predictive mechanisms

“…Within a centralized framework in our previous work [24], the future dynamics of each node can be easily derived provided that the current global state and topology of the whole network are available. However, practically, an individual usually lacks such global knowledge and can only observe its neighbors.…”

“…[19][20][21][22][23], which strongly support the conjecture of the existence of some predictive mechanisms inside abundant biogroups. To answer the second question, as the preliminary work, we showed in our previous paper [24] that centralized predictive mechanism can yield ultrafast consensus without changing the communication topology. To further our investigation, we demonstrate that, by introducing some decentralized predictive mechanisms, it is possible to either significantly enhance the consensus speed obtainable with a fixed communication energy or to decrease the communication energy required to ensure a prescribed consensus speed.…”

“…Thus, each node needs to store sufficiently long historical state sequence of its neighbors and itself. iii) We assume that the sampling and decisionmaking time of all the nodes are synchronized, which is a common assumption for many existing results in literature concerning discrete-time analysis of collective behaviors [3,8,12,14,15,24]. However, even for the asynchronous case, our method still works since the dynamical relationship α ij extracted from neighboring interactions by eq.…”

Ultra-fast formation control of high-order discrete-time multi-agent systems based on multi-step predictive mechanism

“…However, in natural bio-groups, individuals typically have some higher-level intelligence, namely predictive intelligence, which is the ability of predicting the future information of some group members based on their past and current information [11,12]. Motivated by the above analysis, using the local neighbor- error knowledge, a multi-step regulation-error predictive mechanism is established.…”