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| Distributed solving Sylvester equations with fractional order dynamics |
| SongsongCheng,ShuLiang,YuanFan |
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| (Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Electrical Engineering and Automation, Anhui University, Hefei 230601, Anhui, China;Key Laboratory of Knowledge Automation for Industrial Processes of Ministry of Education, School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China) |
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| DOI：https://doi.org/10.1007/s11768-021-00044-0 |
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| 基金项目:This work was supported in part by the National Natural Science Foundation of China (Nos. 61903027, 61973002), and in part by the National Postdoctoral Program for Innovative Talents (BX20180346), and in part by the General Financial Grant from the China Postdoctoral Science Foundation (2019M660834), and in part by the Anhui Provincial Natural Science Foundation (No. 2008085J32). |
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| Distributed solving Sylvester equations with fractional order dynamics |
| Songsong Cheng,Shu Liang,Yuan Fan |
| (Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Electrical Engineering and Automation, Anhui University, Hefei 230601, Anhui, China;Key Laboratory of Knowledge Automation for Industrial Processes of Ministry of Education, School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China) |
| Abstract: |
| This paper addresses distributed computation Sylvester equations of the form AX + XB = C with fractional order dynamics.
By partitioning parameter matrices A, B and C, we transfer the problem of distributed solving Sylvester equations as
two distributed optimization models and design two fractional order continuous-time algorithms, which have more design
freedom and have potential to obtain better convergence performance than that of the existing first order algorithms. Then,
rewriting distributed algorithms as corresponding frequency distributed models, we design Lyapunov functions and prove
that the proposed algorithms asymptotically converge to an exact or least squares solution. Finally, we validate the effectiveness
of the proposed algorithms by providing a numerical example |
| Key words: Fractional order calculus · Distributed optimization · Sylvester equation · Frequency distributed model · Convergence |
