SummaryThis paper studies the controllability of multiagent systems based on path and cycle graphs. For paths or cycles, sufficient and necessary conditions are presented for determining the locations of leaders under which the controllability can be realized. Specifically, the controllability of a path is shown to be determined by a set generated only from its odd factors, and the controllability of a cycle is determined by whether the distance between 2 leaders belongs to a set generated from its even (odd) factors when the number of its nodes is even (odd). For both graphs, the dimension of the controllable subspace is also derived. Moreover, the technique used in the derivation of the above results is further used to get sufficient and necessary conditions for several different types of graphs generated from path and cycle topologies. These types of graphs can be regarded as typical topologies in the study of multiagent controllability, and accordingly the obtained results have meaningful enlightenment for the research in this field.

Stabilizing multiagent systems including unstable agents shows the advantage of cooperation. This paper addresses the problem of stabilization of heterogeneous multiagent systems. Under cycle graphs, a sufficient condition for the stabilization problem via harmonic control is provided and an algorithm of designing the interconnection gains is presented. Furthermore, a sufficient and necessary condition for stabilization problem via harmonic control under cycle graphs is first given when the graph contains less than 5 nodes.

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This paper studies the controllability problem of signed networks which is presented by weighted and directed signed graphs. Graph partitions such as structural balance and almost equitable partitions (AEPs) are studied. We generalize the definition of AEPs to any graphs, directed or undirected, signed or unsigned, with or without edge weights. Based on AEP theory, a graph-theoretic necessary condition is proposed for the controllability of directed signed networks and an algorithm is given for the computation of the coarsest partition. Besides, the upper bound on the controllable subspace is derived when the system is uncontrollable.

An average bit error ratio (ABER) performance model for multiple phase shift keying (MPSK) based on a balanced detector with a fiber is presented in the free-space link for the first time. The Johnson S B probability distribution function (pdf), to the best of our knowledge, is first experimentally explored, which can be used to describe the fading characteristics of an optical signal coupled into a single-mode fiber (SMF) in an atmospheric turbulence channel. Subsequently, an ABER expression is established by combining the photon characteristics of the balanced detector with the fiber. The numerical results show that the system has the most superior ABER performance when the splitting ratio is 0.5 and the quantum efficiency of the two photodetectors is equal. Moreover, the communication performances can be optimized by adjusting parameters, such as increasing the system bandwidth, selecting the appropriate modulation order, and improving the received optical power. Finally, the MPSK-signal-to-noise-ratio (SNR) model is also studied to evaluate system communication performance. Through our asymptotic analysis, if the required ABER falls below the 7% forward error correction (FEC) limit of 3.8 × 10 −3 , the SNR should maintain at least 38 dB or more, while the normalized fluctuation variance deteriorates to 5.2441. This paper provides a parameter reference for designing the MPSK free-space optical (FSO) communication system, especially the fiber-coupling receiver.