Distributed Optimal Resource Allocation for High-Order Nonlinear Multiagent Systems Over Unbalanced Digraphs

In this article, we consider the distributed optimal resource allocation problem with multiple coupled equality constraints for strict-feedback multiagent systems (MASs) over unbalanced digraphs. To solve this problem, a novel integrated distributed control strategy consisting of a set of optimal reference generators and a group of tracking controllers is proposed. The reference generator is based on the estimation of the left eigenvector of the Laplacian matrix and is suitable for unbalanced digraphs. Moreover, the backstepping design technique is efficiently combined with the distributed optimization scheme, leading to a systematic solution for the high-order nonlinear MAS. It is proven that all the outputs of the MAS exponentially converge to the optimal solution of the resource allocation problem under the proposed control. Compared with the existing optimal resource allocation strategies for MASs, the proposed control strategy is applicable to high-order nonlinear MASs and shows favorable exponential convergence, even for unbalanced digraphs. Finally, the simulation results illustrate the above-mentioned theoretical findings.