Distributed Optimal Consensus Control for a Class of Uncertain Nonlinear Multiagent Networks With Disturbance Rejection Using Adaptive Technique

In this article, we consider the distributed optimal consensus problem under nominal and nonfragile cases for a class of minimum-phase uncertain nonlinear systems with unity-relative degree and disturbances generated by an external autonomous system. The involved cost function is the sum of all local cost functions associated with each individual agent. Two different edge-based distributed adaptive algorithms utilizing the internal model principle are designed to solve the problem in a fully distributed manner. Graph theory, nonsmooth analysis, convex analysis, and the Lyapunov theory are employed to show that the proposed algorithms converge accurately to the optimal solution of the considered problem. Finally, an example involving the dynamics of a Lorenz-type system is provided to demonstrate the effectiveness of the obtained results. This work was supported in part by the National Natural Science Foundation of China under Grant 61473055 and Grant 61773089, in part by the Fundamental Research Funds for the Central Universities under Grant DUT17ZD227, and in part by the Youth Star of Dalian Science and Technology under Grant 2015R052 and Grant 2016RQ014.