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In this paper, a distributed adaptive finite-time consensus (FTC) control protocol for a high-order multi-agent system (MAS) with intermittent communications under switching topologies is proposed. Meanwhile, considering the problem of heterogeneous unknown nonlinearities and other uncertain disturbances, the adaptive neural network and the sliding mode control method are used to compensate the nonlinearity of each agent separately. The agents are homogeneous, so the system has symmetry. The switching topologies considered in this paper are asymmetric. Compared with consensus protocol for asymptotic convergence, simulation results show that the proposed method can effectively solve the presence of the nonlinear and accelerate the convergence speed of the system so that an FTC can be reached. [ABSTRACT FROM AUTHOR]

Vertex concavity-convexity detection for spatial objects is a basic algorithm of computer graphics, as well as the foundation for the implementation of other graphics algorithms. In recent years, the importance of the vertex concavity-convexity detection algorithm for three-dimensional (3D) spatial objects has been increasingly highlighted, with the development of 3D modeling, artificial intelligence, and other graphics technologies. Nonetheless, the currently available vertex concavity-convexity detection algorithms mostly use two-dimensional (2D) polygons, with limited research on vertex concavity-convexity detection algorithms for 3D polyhedrons. This study investigates the correlation between the outer product and the topology of the spatial object based on the unique characteristic that the outer product operation in the geometric algebra has unified and definitive geometric implications in space, and with varied dimensionality. Moreover, a multi-dimensional unified vertex concavity-convexity detection algorithm framework for spatial objects is proposed, and this framework is capable of detecting vertex concavity-convexity for both 2D simple polygons and 3D simple polyhedrons. [ABSTRACT FROM AUTHOR]