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Continuous distributed algorithms for solving linear equations in finite time
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DOI：10.1016/j.automatica.2019.108755.png)
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Abstract
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This paper studies the distributed algorithms to obtain a solution of the linear equation Ax = b in finite time (FT) over a multi-agent network. In order to guarantee the settling time without depending on the initial states, the fixed-time (FxT) distributed algorithms are also provided to obtain a solution within a globally bounded time. Specifically, three distributed nonlinear algorithms are developed. The first one is designed to achieve FT/FxT consensus on a solution with special initialization. The second is to obtain the solution in FT/FxT with free initialization by first driving the local states to satisfy the special initialization in FT/FxT time. The last one is to guarantee the FT/FxT convergence to a solution closest to specific points when multiple solutions exist. Finally, three case studies are performed to show the effectiveness of the proposed algorithms. (C) 2019 Elsevier Ltd. All rights reserved.
Keywords:
Distributed algorithms
Finite/fixed-time consensus
Multi-agent networks
Linear equations
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