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We consider the control of formations of a leader-follower network, where the objective is to steer a team of multiple mobile agents into a formation of variable size. We assume that the shape description of the formation is known to all the agents, which is captured by a complex-valued Laplacian associated with the sensing graph, but the size scaling of the formation is not known or only known to two agents, called the leaders in the network. A distributed linear control strategy is developed in this paper such that the agents converge to the desired formation shape, for which the size of the formation is determined by the two leaders. Moreover, in order to make all agents in a formation move with a common velocity, the distributed control law also incorporates a velocity consensus component, which is implemented with the help of a communication network that may, in general, be of different topology from the sensing graph. Both the setup of single-integrator kinematics and the one of double-integrator dynamics are addressed in the same framework except that the acceleration control in the double-integrator setup has an extra damping term.

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This paper investigates two formation control problems for a leader-follower network in 3-D. One is called the formation marching control problem, the objective of which is to steer the agents to maintain a target formation shape while moving with the synchronized velocity. The other one is called the formation rotating control problem, whose goal is to drive the agents to rotate around a common axis with a target formation. For the above two problems, we consider directed and switching sensing topologies while the communication is assumed to be bidirectional and switching. We develop approaches utilizing barycentric coordinates toward these two problems. Local control laws and graphical conditions are acquired to ensure global convergence in both scenarios.

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This paper focuses on the economic power dispatch problem in a smart grid by using the distributed consensus with event-triggered communication mechanism based on continuous-time multi-agent systems over balanced directed networks, where there are many generation units working cooperatively to achieve an optimal solution. The event-triggered communication mechanism means that the information transmission between agents is triggered by event instead of time. The triggering condition and algorithm for each agent are fully decentralized. At each instant time, each agent updates its state by employing the states collected from itself and its neighboring agents at their last triggering time. Finally, two examples are given to analyze the feasibility of above proposed algorithm.

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