Exponential Convergence of Distributed Optimal Coordination for Nonlinear Multiagent Systems Under Directed Graphs

In this article, the distributed optimal coordination problem of second-order uncertain nonlinear multiagent systems, which aims to satisfy a global constrained optimal objective, is formulated and investigated. To solve this problem, a couple of novel proportional–integral (PI)-type control laws are explored. Specifically, a gradient-descent-based PI control law is developed for the weight-balanced graph. Furthermore, by introducing the estimator of the left eigenvector of the Laplacian matrix, the proposed method is extended to the case of an unbalanced graph. Compared with the existing optimal coordination algorithms over nonlinear multiagent systems, our algorithm exhibits the favorable exponential convergence property, albeit employing relaxed balanced/unbalanced directed communication topologies. Two numerical simulations are provided to demonstrate the theoretical results.