Distributed Optimization of Nonlinear Multi-Agent Systems: A Small-Gain Approach

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

Research output: Contribution to journalArticlepeer-review


This paper studies the distributed optimal output agreement problem for multi-agent 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 paper 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 multi-agent system is considered as a dynamical network, and Sontag's input-to-state stability (ISS) is employed to characterize the interconnections. It is shown that output agreement in multi-agent 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 (PI) loops. A numerical example is employed to show the effectiveness of the design.

Original languageEnglish (US)
JournalIEEE Transactions on Automatic Control
StateAccepted/In press - 2021


  • Convergence
  • Linear programming
  • Multi-agent systems
  • Nonlinear dynamical systems
  • Optimal output agreement
  • Optimization
  • Topology
  • Uncertainty
  • input-to-state stability (ISS)
  • multi-agent systems
  • nonlinear PI control
  • nonlinear uncertain dynamics

ASJC Scopus subject areas

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


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