Distributed Continuous-Time Algorithm for Time-Varying Optimization With Affine Formation Constraints

In this article, we investigate a continuous-time distributed optimization problem with time-varying cost functions and affine formation constraints, which are described by the stress matrices rather than the standard Laplacians. The objective is to minimize the sum of local time-varying cost functi...

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Published in:	IEEE transactions on automatic control Vol. 68; no. 4; pp. 2615 - 2622
Main Authors:	Wu, Chu, Fang, Hao, Zeng, Xianlin, Yang, Qingkai, Wei, Yue, Chen, Jie
Format:	Journal Article
Language:	English
Published:	New York IEEE 01.04.2023 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Affine formation Affine transformations Algorithms Cost function Costs fixed-time estimator gradient tracking Laplace equations Stress time-varying optimization Time-varying systems Tracking errors Trajectory Trajectory optimization
ISSN:	0018-9286, 1558-2523
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Abstract	In this article, we investigate a continuous-time distributed optimization problem with time-varying cost functions and affine formation constraints, which are described by the stress matrices rather than the standard Laplacians. The objective is to minimize the sum of local time-varying cost functions, each of which is known by only one individual agent. The optimal solution is a time-varying affine transformation of a nominal configuration rather than some constants. To tackle the difficulty caused by the dynamic aspect of the local cost functions and handle affine formation constraints, the fixed-time distributed estimator and distributed gradient tracking technique are developed, respectively, to compensate the time variation of solution trajectory and calculate the weighted sum of local gradients to eliminate the tracking error. The time-varying optimal solution trajectory is thus accurately tracked with the proposed estimator-based gradient tracking algorithm. Using appropriately chosen coefficients, the tracking error is guaranteed to vanish at an exponential rate. The proposed estimator-based gradient tracking algorithm is further validated through numerical simulations.
AbstractList	In this article, we investigate a continuous-time distributed optimization problem with time-varying cost functions and affine formation constraints, which are described by the stress matrices rather than the standard Laplacians. The objective is to minimize the sum of local time-varying cost functions, each of which is known by only one individual agent. The optimal solution is a time-varying affine transformation of a nominal configuration rather than some constants. To tackle the difficulty caused by the dynamic aspect of the local cost functions and handle affine formation constraints, the fixed-time distributed estimator and distributed gradient tracking technique are developed, respectively, to compensate the time variation of solution trajectory and calculate the weighted sum of local gradients to eliminate the tracking error. The time-varying optimal solution trajectory is thus accurately tracked with the proposed estimator-based gradient tracking algorithm. Using appropriately chosen coefficients, the tracking error is guaranteed to vanish at an exponential rate. The proposed estimator-based gradient tracking algorithm is further validated through numerical simulations.
Author	Fang, Hao Chen, Jie Yang, Qingkai Wu, Chu Wei, Yue Zeng, Xianlin
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SubjectTerms	Affine formation Affine transformations Algorithms Cost function Costs fixed-time estimator gradient tracking Laplace equations Stress time-varying optimization Time-varying systems Tracking errors Trajectory Trajectory optimization
Title	Distributed Continuous-Time Algorithm for Time-Varying Optimization With Affine Formation Constraints
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