In this paper, we propose a strategy for the control of mobile chaotic oscillators by adaptively rewiring connections between nearby agents with local information. In contrast to the dominant adaptive control schemes where coupling strength is adjusted continuously according to the states of the oscillators, our method does not request adaption of coupling strength. As the resulting interaction structure generated by this proposed strategy is strongly related to unidirectional chains, by investigating synchronization property of unidirectional chains, we reveal that there exists a certain coupling range in which the agents could be controlled regardless of the length of the chain. This feature enables the adaptive strategy to control the mobile oscillators regardless of their moving speed. Compared with existing adaptive control strategies for networked mobile agents, our proposed strategy is simpler for implementation where the resulting interaction networks are kept unweighted at all time. Synchronization is a ubiquitous collective behavior, widely found in biological, physical, and social systems [1] [2] [3] [4] [5] [6] . An issue of particular relevance is the control of networked systems, so as to target them towards specific, collective, and desired functionings. When the topology of connections among the units of a network is fixed, various strategies can be adopted, such as: i) regulating the strength of the coupling between the graph's components [7] [8] [9] [10] [11] [12] [13] , ii) applying a time delay 14, 15 , iii) changing adaptively the nodes' interaction 16 , iv) pinning specific sequences of network's components [17] [18] [19] . With the rapid development of technology in mobile devices, synchronization and control of mobile agents becomes, however, an issue of primary importance [20] [21] [22] . Conditions for synchronization of networks with time-varying structure under various circumstances have been studied. Such conditions include that the time-varying structures are always small world 23, 24 , oscillators perform random walk on networked infrastructure [25] [26] [27] , oscillators could move on a one-dimensional ring 28 , oscillators are allowed to jump randomly in the space 29 , etc. A good study of the condition of stable synchronization for fast-switching networks, where the network structure changes much faster than the unit dynamics, can be found in ref. 30 , while a study for slow-switching networks is presented in ref. 31 . Further, the compound effect of different time scales between structure dynamics and unit dynamics has been studied in ref. . The problem of controlling networked mobile oscillators has received many research interests [33] [34] [35] [36] [37] . However, moving-agent systems commonly have features of spatial distribution, communication constraints, and limited sensing capacity, which makes centralized control strategies generally too expensive or even infeasible to be implemented in practice. Therefore, many adaptive control strategies which require only local information, termed as decentralized strategies, have been proposed in the last decade. For instance, an adaptive strategy has been designed for the consensus of networked moving agents 38 . Further, the situation of input saturation has been taken into consideration 39 . Because of the advantages of the decentralized method, adaptive control strategies have also been extensively developed for networks with static structures [40] [41] [42] . However, most existing adaptive control strategies are realized by continuously adjusting coupling strength between agents, here we referred as coupling adaption strategy. In this paper, we propose a strategy where agents may adaptively choose neighboring ones to establish temporary connections without tunning coupling strength, which we refer to as connection adaptation strategy. We prove that the temporary networks generated from our strategy have the same synchronization stability as that of the static networks with the same Laplacian spectrum. We further show that the resulting structure is closely related to unidirectional chains. Our study suggests that for such chains there exists a certain range of coupling strength within which the whole chain could be controlled
Recently, a strategy has been proposed in which units may adaptively choose neighboring ones to establish temporary connections without tuning coupling strength or control gains REF .
Connection adaption for control of networked mobile chaotic agents
Scientific Reports
Scientific Reports
Computer Science Medicine