Distributed continuous-time time-varying optimization for networked Lagrangian systems with quadratic cost functions

IF 4.8 2区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS
Yong Ding , Hanlei Wang , Wei Ren
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Abstract

In this paper, the distributed time-varying optimization problem is investigated for networked Lagrangian systems with parametric uncertainties. Usually, in the literature, to address some distributed control problems for nonlinear systems, a networked virtual system is constructed, and a tracking algorithm is designed such that the agents’ physical states track the virtual states. It is worth pointing out that such an idea requires the exchange of the virtual states and hence necessitates communication among the group. In addition, due to the complexities of the Lagrangian dynamics and the distributed time-varying optimization problem, there exist significant challenges. This paper proposes distributed time-varying optimization algorithms that achieve zero optimum-tracking errors for the networked Lagrangian agents without the communication requirement. The main idea behind the proposed algorithms is to construct a reference system for each agent to generate a reference velocity using absolute and relative physical state measurements with no exchange of virtual states needed, and to design adaptive controllers for Lagrangian systems such that the physical states are able to track the reference velocities and hence the optimal trajectory. The algorithms introduce mutual feedback between the reference systems and the local controllers via physical states/measurements and are amenable to implementation via local onboard sensing in a communication unfriendly environment. Specifically, first, a base algorithm is proposed to solve the distributed time-varying optimization problem for networked Lagrangian systems under switching graphs. Then, based on the base algorithm, a continuous function is introduced to approximate the signum function, forming a continuous distributed optimization algorithm and hence removing the chattering. Such a continuous algorithm is convergent with bounded ultimate optimum-tracking errors, which are proportion to approximation errors. Finally, numerical simulations are provided to illustrate the validity of the proposed algorithms.

具有二次成本函数的网络拉格朗日系统的分布式连续时间时变优化
本文研究了具有参数不确定性的网络拉格朗日系统的分布式时变优化问题。通常,文献中为了解决一些非线性系统的分布式控制问题,会构建一个网络虚拟系统,并设计一种跟踪算法,使代理的物理状态跟踪虚拟状态。值得指出的是,这种想法需要交换虚拟状态,因此需要小组之间进行通信。此外,由于拉格朗日动力学和分布式时变优化问题的复杂性,存在着巨大的挑战。本文提出了分布式时变优化算法,可在无需通信的情况下实现网络化拉格朗日代理的零最佳跟踪误差。所提算法的主要思想是为每个代理构建一个参考系统,利用绝对和相对物理状态测量值生成参考速度,无需交换虚拟状态,并为拉格朗日系统设计自适应控制器,使物理状态能够跟踪参考速度,从而实现最优轨迹。这些算法通过物理状态/测量值在参考系统和本地控制器之间引入了相互反馈,并可在通信不友好的环境中通过本地机载传感实现。具体来说,首先提出了一种基础算法,用于解决切换图下网络化拉格朗日系统的分布式时变优化问题。然后,在基础算法的基础上,引入一个连续函数来近似符号函数,形成一个连续的分布式优化算法,从而消除颤振。这种连续算法是收敛的,其终极最优跟踪误差是有界的,与近似误差成正比。最后,通过数值模拟说明了所提算法的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Automatica
Automatica 工程技术-工程:电子与电气
CiteScore
10.70
自引率
7.80%
发文量
617
审稿时长
5 months
期刊介绍: Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field. After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience. Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.
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