Time-domain response of nabla discrete fractional order systems

This paper investigates the time--domain response of nabla discrete fractional order systems by exploring several useful properties of the nabla discrete Laplace transform and the discrete Mittag--Leffler function. In particular, we establish two fundamental properties of a nabla discrete fractional order system with nonzero initial instant: i) the existence and uniqueness of the system time--domain response; and ii) the dynamic behavior of the zero input response. Finally, one numerical example is provided to show the validity of the theoretical results.Comment: 13 pages, 6 figure

Distributed optimization for multi-agent system over unbalanced graphs with linear convergence rate

summary:Distributed optimization over unbalanced graphs is an important problem in multi-agent systems. Most of literatures, by introducing some auxiliary variables, utilize the Push-Sum scheme to handle the widespread unbalance graph with row or column stochastic matrix only. But the introduced auxiliary dynamics bring more calculation and communication tasks. In this paper, based on the in-degree and out-degree information of each agent, we propose an innovative distributed optimization algorithm to reduce the calculation and communication complexity of the conventional Push-Sum scheme. Furthermore, with the aid of small gain theory, we prove the linear convergence rate of the proposed algorithm

A stochastic mirror-descent algorithm for solving AXB=CAXB=C over an multi-agent system

summary:In this paper, we consider a distributed stochastic computation of $AXB=C$ with local set constraints over an multi-agent system, where each agent over the network only knows a few rows or columns of matrixes. Through formulating an equivalent distributed optimization problem for seeking least-squares solutions of $AXB=C$, we propose a distributed stochastic mirror-descent algorithm for solving the equivalent distributed problem. Then, we provide the sublinear convergence of the proposed algorithm. Moreover, a numerical example is also given to illustrate the effectiveness of the proposed algorithm

A penalty ADMM with quantized communication for distributed optimization over multi-agent systems

summary:In this paper, we design a distributed penalty ADMM algorithm with quantized communication to solve distributed convex optimization problems over multi-agent systems. Firstly, we introduce a quantization scheme that reduces the bandwidth limitation of multi-agent systems without requiring an encoder or decoder, unlike existing quantized algorithms. This scheme also minimizes the computation burden. Moreover, with the aid of the quantization design, we propose a quantized penalty ADMM to obtain the suboptimal solution. Furthermore, the proposed algorithm converges to the suboptimal solution with an $O(\frac{1}{k})$ convergence rate for general convex objective functions, and with an R-linear rate for strongly convex objective functions