Achieving distributed convex optimization within prescribed time for high-order nonlinear multiagent systems
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866915888167387136 |
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| author | Zuo, Gewei Zhu, Lijun Wang, Yujuan Chen, Zhiyong Song, Yongduan |
| author_facet | Zuo, Gewei Zhu, Lijun Wang, Yujuan Chen, Zhiyong Song, Yongduan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_11413 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Achieving distributed convex optimization within prescribed time for high-order nonlinear multiagent systems Zuo, Gewei Zhu, Lijun Wang, Yujuan Chen, Zhiyong Song, Yongduan Optimization and Control Systems and Control 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. |
| title | Achieving distributed convex optimization within prescribed time for high-order nonlinear multiagent systems |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2407.11413 |