Distributed Optimization of Nonlinear Multiagent Systems: A Small-Gain Approach

Tengfei Liu, Zhengyan Qin, Yiguang Hong, Zhong Ping Jiang

Research output: Contribution to journalArticlepeer-review


This article studies the distributed optimal output agreement problem for multiagent systems described by uncertain nonlinear models. By using the partial information of an objective function, the design aims to steer the outputs of the agents to an agreement on the optimal solution to the objective function. To solve this problem, this article introduces distributed coordinators to calculate the desired outputs, and designs reference-tracking controllers for the agents to follow the desired outputs. To deal with the nonlinear uncertain dynamics, the closed-loop multiagent system is considered as a dynamical network, and Sontag's input-to-state stability is employed to characterize the interconnections. It is shown that output agreement in multiagent nonlinear systems is achievable by means of distributed optimal controllers via a small-gain approach. The proposed design features a three-layer architecture, and the reference-tracking controllers can be implemented as successive nonlinear proportional-integral loops. A numerical example is employed to show the effectiveness of the design.

Original languageEnglish (US)
Pages (from-to)676-691
Number of pages16
JournalIEEE Transactions on Automatic Control
Issue number2
StatePublished - Feb 1 2022


  • Input-to-state stability (ISS)
  • Multiagent systems
  • Nonlinear proportional-integral (PI) control
  • Nonlinear uncertain dynamics
  • Optimal output agreement

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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