Nonsmooth Resource Allocation of Multiagent Systems With Disturbances: A Proximal Approach

This article aims to solve the nonsmooth resource allocation problem in the presence of a global network resource constraint and local set constraints in the framework of multiagent system optimization. It is assumed that multiagent systems are subject to some external disturbances, and the control inputs of the agents satisfy Lispchitz continuity. These two distinguished features render the existing distributed optimization algorithms, especially the subgradient-based algorithms inapplicable due to the employment of discontinuity of subgradients. To solve such a challenging resource allocation problem, a new kind of continuous-time proximal algorithm is designed with the aid of convex optimization theory and the internal-model technique. The proximal algorithm is further augmented by introducing an event-based communication scheme such that the continuous-time communication among the agents is avoided successfully. The theoretical analysis shows that the multiagent systems under the proposed algorithms can converge to the optimal solution of the considered problem, while the external disturbances are rejected. Besides, the Zeno behavior can be excluded for the proximal algorithm with event-based communication. Finally, the numerical simulations are given to verify the established theoretical results.

I. Introduction

Distributed optimization has been extensively investigated via plenty of distributed algorithms in recent years (see [1] and the references therein). In fact, most results have been previously concerned with designing distributed optimization, while the dynamics of agents have received less attention. Recently, distributed optimization with the dynamics of agents has been studied by designing continuous-time control algorithms for many types of multiagent systems, for instance, single-integrator dynamics [2]–[5]; Euler–Lagrange systems [6], [7]; double-integrator dynamics [8]; linear multiagent systems [9]; and nonlinear multiagent systems [10]–[12].