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Signed directed graphs contain both sign and direction information on their edges, providing richer information about real-world phenomena compared to unsigned or undirected graphs. However, analyzing such graphs is more challenging due to their complexity, and the limited availability of existing methods. Consequently, despite their potential uses, signed directed graphs have received less research attention. In this paper, we propose a novel spectral graph convolution model that effectively captures the underlying patterns in signed directed graphs. To this end, we introduce a complex Hermitian adjacency matrix that can represent both sign and direction of edges using complex numbers. We then define a magnetic Laplacian matrix based on the adjacency matrix, which we use to perform spectral convolution. We demonstrate that the magnetic Laplacian matrix is positive semi-definite (PSD), which guarantees its applicability to spectral methods. Compared to traditional Laplacians, the magnetic Laplacian captures additional edge information, which makes it a more informative tool for graph analysis. By leveraging the information of signed directed edges, our method generates embeddings that are more representative of the underlying graph structure. Furthermore, we showed that the proposed method has wide applicability for various graph types and is the most generalized Laplacian form. We evaluate the effectiveness of the proposed model through extensive experiments on several real-world datasets. The results demonstrate that our method outperforms state-of-the-art techniques in signed directed graph embedding. • This paper introduces a novel complex Hermitian adjacency matrix that encodes signed directed graphs using complex numbers. • It proposes a magnetic Laplacian matrix via the Hermitian and proves its positive semi-definite property. • With the magnetic Laplacian, this paper define a spectral graph convolution operation. • The proposed convolution enjoys wide applicability for several graph types from vanilla to signed directed. • SD-GCN shows superior performance in several datasets compare to other SOTAs. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a multi-impulsive formation control strategy using orbit energy-matching and relative angular momentum vector between leader and follower satellites. These conservative parameters (energy and angular momentum) provide analytical and global solutions for orbital maneuver design without relying on Gauss variational equations. The relationship with orbit element differences is discussed in the simplifying assumptions. The proposed approach is free from small variation assumptions, so that it is suitable for handling even the case of large error corrections. General limitations of impulse control and associated compensation maneuvers are also addressed. [Copyright &y& Elsevier]

Abstract: Spacecraft attitude estimation based on the nonlinear unscented filter is addressed to fully utilize capabilities of the unscented transformation. To overcome significant computational load, an efficient technique is proposed by appropriately eliminating correlation between random variables. This modification leads to a considerable reduction of computational burden in matrix square-root calculation for most nonlinear systems. The unscented filter makes use of a set of sample points to predict mean and covariance. For attitude estimation based on quaternions, an approach to computing quaternion means from sampled quaternions with guarantee of the normalization constraint is described by using a constrained optimization technique. Finally, the performance of the new approach is demonstrated by attitude determination using a star tracker and rate-gyro measurements. [Copyright &y& Elsevier]

Abstract: An adaptive control technique can be applicable to reorient spacecraft with uncertain properties such as mass, inertial and various misalignments. A nonlinear quaternion feedback controller is chosen as a baseline attitude controller. A linearly added adaptive input supported by neural networks to the baseline controller can estimate and eliminate the uncertain spacecraft property adaptively. The normalized input neural networks (NINNs) are examined for reliable computation of the adaptive input. The newly defined learning rules of the neural networks are established appropriately for a spacecraft. To prove the stability of the closed-loop dynamics with the control law, Lyapunov stability theory is considered. As a result, the proposed approach results in the uniform ultimate boundedness in tracking error and robustness of the chattering and the singularity problems. [Copyright &y& Elsevier]