In this paper, we consider a multi-agent consensus problem with an active leader and variable interconnection topology. The state of the considered leader not only keeps changing but also may not be measured. To track such a leader, a neighbor-based local controller together with a neighbor-based state-estimation rule is given for each autonomous agent. Then we prove that, with the proposed control scheme, each agent can follow the leader if the (acceleration) input of the active leader is known, and the tracking error is estimated if the input of the leader is unknown.

Tumour-necrosis factor (TNF) receptor-associated factor 6 (TRAF6) is the only TRAF family member that participates in signal transduction of both the TNF receptor (TNFR) superfamily and the interleukin-1 receptor (IL-1R)/Toll-like receptor (TLR) superfamily; it is important for adaptive immunity, innate immunity and bone homeostasis. Here we report crystal structures of TRAF6, alone and in complex with TRAF6-binding peptides from CD40 and TRANCE-R (also known as RANK), members of the TNFR superfamily, to gain insight into the mechanism by which TRAF6 mediates several signalling cascades. A 40 degrees difference in the directions of the bound peptides in TRAF6 and TRAF2 shows that there are marked structural differences between receptor recognition by TRAF6 and other TRAFs. The structural determinant of the petide TRAF6 interaction reveals a Pro-X-Glu-X-X-(aromatic/acidic residue) TRAF6-binding motif, which is present not only in CD40 and TRANCE-R but also in the three IRAK adapter kinases for IL-1R/TLR signalling. Cell-permeable peptides with the TRAF6-binding motif inhibit TRAF6 signalling, which indicates their potential as therapeutic modulators. Our studies identify a universal mechanism by which TRAF6 regulates several signalling cascades in adaptive immunity, innate immunity and bone homeostasis.

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In this paper, we consider a leader-following consensus problem of a group of autonomous agents with time-varying coupling delays. Two different cases of coupling topologies are investigated. At first, a necessary and sufficient condition is proved in the case when the interconnection topology is fixed and directed. Then a sufficient condition is proposed in the case when the coupling topology is switched and balanced. Numerical examples are also given to illustrate our results.

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