An exponentially convergent distributed algorithm for resource allocation problem

Abstract

In this paper, the distributed resource allocation problem over undirected networks, considering box constraints and demand–supply constraints, is studied. Furthermore, each agent has one private cost function that is only known by itself. The aim is to minimize the sum of all local cost functions in a distributed manner while meeting the constraints. To solve the dispatch problem, a continuous‐time distributed algorithm with fixed step‐size is proposed. After that, a modified distributed algorithm of discrete‐time multi‐agent system is provided. Moreover, the proposed algorithms obtain the global optimal solution with an exponential convergence speed by the conventional Lyapunov methods. Finally, several simulations of IEEE‐14 bus are presented to validate and illustrate the proposed designed algorithm.

Optimality Condition and Distributed Optimization for Economic Dispatch Using a Novel Weighted Incremental Cost Consensus Approach

“…(2020), the present approach can be extended for event-triggered communication, rather than the time-triggered approach, for the efficient bandwidth utilization. Furthermore, the presented approach can be extended for exponential rate of the optimization, based on the results of Shi et al (2021), for controlling the convergence rate parameter.…”

“…Recently, economic dispatch has been addressed inZhao et al (2018) andShi et al (2020) for saving the communication bandwidth through an even-triggering mechanism. Another interesting study ofShi et al (2021) has developed an optimization protocol for exponential convergence. Compared to these results, the presented approach considers an optimization problem by considering a different weighted cost function.…”

Predefined‐time distributed event‐triggered algorithms for resource allocation

“…Lemma [59] Under Assumption 1, let $$Q={[r,R]}^{T}\in {\mathbb{R}}^{n\times n}$$ be an orthogonal matrix with $$r=\frac{1}{\sqrt{n}}{1}_{n}$$ and $$R\in {\mathbb{R}}^{n\times (n-1)}$$, then we have $$R{{\Lambda}}_{1}^{-1}{R}^{T}L=LR{{\Lambda}}_{1}^{-1}{R}^{T}={K}_{n}$$, where $${K}_{n}={I}_{n}-\frac{1}{n}{1}_{n}{1}_{n}^{T}$$ and Λ 1 = diag{ ρ 2 ( L ), …, ρ n ( L )}.…”

Distributed Resource Allocation Algorithm for General Linear Multiagent Systems

“…In contrast to the previous exterior point method, an initialization-free distributed resource allocation algorithm is designed by the interior point penalty function method in [37]. A novel projection operator approach was proposed to accelerate the convergence speed in [39], in which the dual variable directly determines the state variable. The resource allocation problem over the unbalanced directed network was solved using the consensus scheme to obtain the left eigenvector of the corresponding Laplacian matrix [40].…”