Search

This paper investigates the cooperative output regulation problem for heterogeneous multiagent systems (MASs) under switching topology. Two novel distributed event-triggered adaptive control strategies based on state feedback and output feedback are developed, which can avoid using the minimal nonzero eigenvalue of Laplacian matrix associated with global system topologies. It is shown that under the proposed control protocols, MASs could achieve asymptotic tracking and disturbance rejection, and meanwhile, the amount of transmission data and communication cost among agents can be reduced. Then, the leader-following consensus problem of MASs is given as an application of our main results. Finally, an example is presented to verify the effectiveness of the proposed control schemes. [ABSTRACT FROM AUTHOR]

This article aims to point out an error in the concerned paper and a possible correction to address the error. The correction is achieved by several revisions made on the corresponding assumption, event-triggering function, adaptive laws, and event-triggered control law. [ABSTRACT FROM AUTHOR]

We explore higher-form symmetries of M- and F-theory compactified on elliptic fibrations, determined by the topology of their asymptotic boundaries. The underlying geometric structures are shown to be equivalent to known characterizations of the gauge group topology in F-theory via Mordell-Weil torsion and string junctions. We further study dimensional reductions of the 11d Chern-Simons term in the presence of torsional boundary G4-fluxes, which encode background gauge fields of center one-form symmetries in the lower-dimensional effective gauge theory. We find contributions that can be interpreted as 't Hooft anomalies involving the one-form symmetry which originate from a fractionalization of the instanton number of non-Abelian gauge theories in F-/M-theory compactifications to 8d/7d and 6d/5d. [ABSTRACT FROM AUTHOR]

Compactifications of the Chaudhuri-Hockney-Lykken (CHL) string to eight dimensions can be characterized by embeddings of root lattices into the rank 12 momentum lattice ΛM, the so-called Mikhailov lattice. Based on these data, we devise a method to determine the global gauge group structure including all U(1) factors. The key observation is that, while the physical states correspond to vectors in the momentum lattice, the gauge group topology is encoded in its dual. Interpreting a nontrivial π1(G) ≡ Z for the non-Abelian gauge group G as having gauged a Z 1-form symmetry, we also prove that all CHL gauge groups are free of a certain anomaly [1] that would obstruct this gauging. We verify this by explicitly computing Z for all 8D CHL vacua with rank (G) = 10. Since our method applies also to T² compactifications of heterotic strings, we further establish a map that determines any CHL gauge group topology from that of a "parent" heterotic model. [ABSTRACT FROM AUTHOR]