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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Veröffentlicht in:IEEE transactions on automatic control Jg. 68; H. 4; S. 2615 - 2622
Hauptverfasser: Wu, Chu, Fang, Hao, Zeng, Xianlin, Yang, Qingkai, Wei, Yue, Chen, Jie
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York IEEE 01.04.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
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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Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2022.3190054