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In this paper, the formation control of networks of multiple agents is studied via controllability, where the network is under leader-follower structure with some agents taking the leader role and others being followers interconnected via neighbor-based rule. It is shown that the controllability of a multi-agent system is uniquely determined by the topology structure of interconnection graph, and the investigation of which comes down to that for a multi-agent system with the interconnection graph being connected. Based on these observations, two kinds of interconnection graph topologies are characterized, under which the network of multiple agents is uncontrollable, revealing to some extent how the controllability, and accordingly the formation control, are affected by the interconnection topology between agents. Finally, a necessary and sufficient condition in terms of eigenvector is presented. The results also touch upon the selection of leaders and are illustrated by several examples.

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Three biomimetic 2Fe2S complexes [{(micro-SCH2)2NCH2(2-C4H3O)}](Fe2(CO)6), [{(micro-SCH2)2 NCH2(2-C4H3S)}](Fe2(CO)6) and [{(micro-SCH2)2NCH2(5-Br-2-C4H2S)}Fe2(CO)6] were prepared as models for the active site of Fe-only hydrogenase by the convergent process from [(micro-S2)Fe2(CO)6] and N,N-bis(hydromethyl)-2-furan and thiophene. The structures of these complexes were identified spectroscopically and crystallographically. The electrochemical behavior of the complexes and was unique as they showed catalytic proton reduction with a low reduction potential at -1.13 and -1.09 V vs Fc/Fc+, respectively, in the presence of HClO4.

Restructuring of supported metal nanoparticles (NPs) (e.g., reshaping and redispersion) is of tremendous interest for the rational design of well-defined catalyst materials, but the underlying mechanism to tune their dynamic behaviors and thus reactivity is still unspecified. Here, we show a crystal-phase-mediated redispersion/reshaping of Pt NPs on TiO2, boosting opposite reactivities in hydrogenation/oxidation reactions. Utilizing a variety of state-of-the-art characterization methods, we unraveled that rutile TiO2 favors the reshaping of Pt NPs into two-dimensional planar geometry, whereas the anatase surface facilitates the redispersion of Pt NPs to single atoms (SAs) upon the same calcination procedure. Environmental transmission electron microscopy and density functional theory calculations were employed to directly visualize the dynamic transformation of Pt NPs and reveal the specific role of TiO2 supports in promoting the stability and diffusion of Pt SAs. As a result, the opposite reactivity was achieved by tuning their distinct restructuring behaviors. Thus, the redispersion of Pt on anatase TiO2 facilitates the selective hydrogenation of phenylacetylene with a high styrene yield of 21.22 × 10–2 s–1, whereas the reshaping on the rutile phase favors the combustion of methane with a turnover frequency as high as 3.11 × 10–2 s–1. Our results therefore open up an effective route for tuning the restructuring behavior of supported metal catalysts and designing catalysts with controlled catalytic structures and reactivities.