This article investigates the positive consensus problem of a special kind of interconnected positive systems over directed graphs. They are composed of multiple fractional-order continuous-time positive linear systems. Unlike most existing works in the literature, we study this problem for the first time, in which the communication topology of agents is described by a directed graph containing a spanning tree. This is a more general and new scenario due to the interplay between the eigenvalues of the Laplacian matrix and the controller gains, which renders the positivity analysis fairly challenging. Based on the existing results in spectral graph theory, fractional-order systems (FOSs) theory, and positive systems theory, we derive several necessary and/or sufficient conditions on the positive consensus of fractional-order multiagent systems (PCFMAS). It is shown that the protocol, which is designed for a specific graph, can solve the positive consensus problem of agents over an additional set of directed graphs. Finally, a comprehensive comparison study of different approaches is carried out, which shows that the proposed approaches have advantages over the existing ones.

This technical note investigates the positive consensus problem of multiagent systems with directed communication topologies, where all the agents have identical continuous-time positive linear dynamics. Existing works of such a problem mainly focus on the case, where networked communication topologies are of either undirected and incomplete graphs, or strongly connected directed graphs. In contrast to them, we study this problem in which the communication topologies of the multiagent system are described by directed graphs each containing a spanning tree, which is a more general and new scenario due to the interplay between the eigenvalues of the Laplacian matrix and the controller gains. Based on the existing results in spectral graph theory and positive linear systems theory, several necessary, and sufficient conditions on positive consensus of the directed multiagent system are derived through using linear matrix inequality techniques. A primal-dual iterative algorithm is developed for the computation of solutions. Finally, several numerical simulations are provided to illustrate the effectiveness of the proposed theoretical results.

Based on cloud-fog computing, a cooperative control method is proposed for an air-ground heterogeneous swarm and the event-triggered strategy is introduced to eliminate the adverse effects of cyber attack. First, an air-ground nonlinear swarm system with aggregation-dispersion properties is built. Simultaneously, for better coordination and scalability of the heterogeneous swarm, a could-fog computing architecture dividing the swarm into two control layers is presented. As the swarm scales up, its susceptibility to random cyber-attacks increases, particularly to Denial of Service (DoS) attacks. Thus, the fog-cloud cooperative control method is proposed to ensure the secure consistency of the swarm under DoS attacks. In this way, a distributed average consensus control law at the fog layer is designed, while a leader-following-based asymptotic consensus control algorithm at the cloud layer is presented. Finally, numerical simulations are performed to verify the correctness and effectiveness of the proposed method, which has the strong robustness and scalability of the large-scale swarm system.