Mathematics > Optimization and Control
arXiv:2407.11413 (math)
[Submitted on 16 Jul 2024 (v1), last revised 27 Nov 2024 (this version, v2)]
Title:Distributed Prescribed-Time Convex Optimization: Cascade Design and Time-Varying Gain Approach
View a PDF of the paper titled Distributed Prescribed-Time Convex Optimization: Cascade Design and Time-Varying Gain Approach, by Gewei Zuo and 2 other authors
View PDFHTML (experimental)Abstract:In this paper, we address the distributed prescribed-time convex optimization (DPTCO) problem for a class of nonlinear multi-agent systems (MASs) under undirected connected graph. A cascade design framework is proposed such that the DPTCO implementation is divided into two parts: distributed optimal trajectory generator design and local reference trajectory tracking controller design. The DPTCO problem is then transformed into the prescribed-time stabilization problem of a cascaded system. Changing Lyapunov function method and time-varying state transformation method together with the sufficient conditions are proposed to prove the prescribed-time stabilization of the cascaded system as well as the uniform boundedness of internal signals in the closed-loop systems. The proposed framework is then utilized to solve robust DPTCO problem for a class of chain-integrator MASs with external disturbances by constructing a novel variables and exploiting the property of time-varying gains. The proposed framework is further utilized to solve the adaptive DPTCO problem for a class of strict-feedback MASs with parameter uncertainty, in which backstepping method with prescribed-time dynamic filter is adopted. The descending power state transformation is introduced to compensate the growth of increasing rate induced by the derivative of time-varying gains in recursive steps and the high-order derivative of local reference trajectory is not required. Finally, theoretical results are verified by two numerical examples.
| Comments: | 13 pages, |
| Subjects: | Optimization and Control (math.OC); Systems and Control (eess.SY) |
| Cite as: | arXiv:2407.11413 [math.OC] |
| (orarXiv:2407.11413v2 [math.OC] for this version) | |
| https://doi.org/10.48550/arXiv.2407.11413 arXiv-issued DOI via DataCite |
Submission history
From: Zuo Gewei [view email][v1] Tue, 16 Jul 2024 06:00:39 UTC (3,841 KB)
[v2] Wed, 27 Nov 2024 00:55:15 UTC (3,918 KB)
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View a PDF of the paper titled Distributed Prescribed-Time Convex Optimization: Cascade Design and Time-Varying Gain Approach, by Gewei Zuo and 2 other authors
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