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This study proposes a secondary voltage and frequency control scheme based on the distributed cooperative control of multi-agent systems. The proposed secondary control is implemented through a communication network with one-way communication links. The required communication network is modelled by a directed graph (digraph). The proposed secondary control is fully distributed such that each distributed generator only requires its own information and the information of its neighbours on the communication digraph. Thus, the requirements for a central controller and complex communication network are obviated, and the system reliability is improved. The simulation results verify the effectiveness of the proposed secondary control for a microgrid test system.

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The problem of determining a collision-free path for a mobile robot moving in a dynamically changing environment is addressed in this paper. By explicitly considering a kinematic model of the robot, the family of feasible trajectories and their corresponding steering controls are derived in a closed form and are expressed in terms of one adjustable parameter for the purpose of collision avoidance. Then, a new collision-avoidance condition is developed for the dynamically changing environment, which consists of a time criterion and a geometrical criterion, and it has explicit physical meanings in both the transformed space and the original working space. By imposing the avoidance condition, one can determine one (or a class of) collision-free path(s) in a closed form. Such a path meets all boundary conditions, is twice differentiable, and can be updated in real time once a change in the environment is detected. The solvability condition of the problem is explicitly found, and simulations show that the proposed method is effective.