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

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.