This article investigates the distributed secure state estimation problem of distributed systems where a set of agents estimates the state cooperatively in the presence of malicious agents. First, a sufficient condition for the solvability of the distributed secure state estimation problem is proposed. Second, based on the obtained condition, a distributed switched gradient descent (DSGD) algorithm is designed to solve the considered problem which is transformed into a distributed optimization problem. With the help of a candidate-removal mechanism, the proposed DSGD algorithm successfully generates reliable state estimates despite malicious agents. Finally, the effectiveness of the proposed algorithm is illustrated by a numerical example.

中文翻译：

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存在恶意代理的分布式安全状态估计

本文研究了分布式系统的分布式安全状态估计问题，其中一组代理在存在恶意代理的情况下协作估计状态。首先，提出了分布式安全状态估计问题可解性的充分条件。其次，基于获得的条件，设计分布式切换梯度下降（DSGD）算法来解决所考虑的问题，并将其转化为分布式优化问题。在候选删除机制的帮助下，尽管存在恶意代理，所提出的 DSGD 算法成功地生成了可靠的状态估计。最后，通过数值例子说明了所提出算法的有效性。