Distributed Convex Optimization Over Nonlinear Networks Under Set Constraints

This article is devoted to the distributed convex optimization problem for a class of nonlinear multiagent systems under set constraints. The optimization objective function is composed of the cost function of each agent, where the individual cost function is only accessible by itself. Due to the co...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 70; no. 7; pp. 4735 - 4742
Main Authors: Zhang, Jing, Liu, Shuai, Xie, Lihua
Format: Journal Article
Language:English
Published: New York IEEE 01.07.2025
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Auxiliary system
Constraints
Convergence
Convex analysis
Convex functions
Convexity
Cost function
Directed graphs
distributed convex optimization
Dynamical systems
Global optimization
Multi-agent systems
Multiagent systems
Nonlinear dynamics
nonlinear multiagent systems
Nonlinear systems
Optimization
projection gradient algorithm
Protocols
Topology
Vectors
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Summary:This article is devoted to the distributed convex optimization problem for a class of nonlinear multiagent systems under set constraints. The optimization objective function is composed of the cost function of each agent, where the individual cost function is only accessible by itself. Due to the complexity of nonlinear dynamics of agents, it is very difficult to solve the optimization problem directly. Therefore, we first propose an auxiliary system for each agent, which is used to seek the solution of the global optimization problem. And we present a novel method to ensure that the states of the auxiliary systems are uniformly bounded. Then, a distributed control protocol is designed for the multiagent systems to enable each agent to track its auxiliary system. It is worthy noting that the auxiliary system and the local tracking controller are coupled and need to be jointly designed. Finally, it is proved that the overall systems are stable and the output of each agent can converge to the solution of the constrained optimization problem. Two examples are provided to validate the effectiveness of the proposed method.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2025.3535578