Distributed optimization algorithm for discrete-time heterogeneous multi-agent systems with nonuniform stepsizes

This paper is devoted to the distributed optimization problem of heterogeneous multi-agent systems, where the communication topology is jointly strongly connected and the dynamics of each agent is the first-order or second-order integrator. A new distributed algorithm is first designed for each agent based on the local objective function and the local neighbors' information that each agent can access. By a model transformation, the original closed-loop system is converted into a time-varying system and the system matrix of which is a stochastic matrix at any time. Then, by the properties of the stochastic matrix, it is proven that all agents' position states can converge to the optimal solution of a team objective function provided the union communication topology is strongly connected. Finally, the simulation results are provided to verify the effectiveness of the distributed algorithm proposed in this paper

A Robust Distributed Model Predictive Control Framework for Consensus of Multi-Agent Systems with Input Constraints and Varying Delays

This paper studies the consensus problem of general linear discrete-time multi-agent systems (MAS) with input constraints and bounded time-varying communication delays. We propose a robust distributed model predictive control (DMPC) consensus protocol that integrates the offline consensus design with online DMPC optimization to exploit their respective advantages. More precisely, each agent is equipped with an offline consensus protocol, which is a priori designed, depending on its immediate neighbors' estimated states. Further, the estimation errors propagated over time due to inexact neighboring information are proved bounded under mild technical assumptions, based on which a robust DMPC strategy is deliberately designed to achieve robust consensus while satisfying input constraints. Moreover, it is shown that, with the suitably designed cost function and constraints, the feasibility of the associated optimization problem can be recursively ensured. We further provide the consensus convergence result of the constrained MAS in the presence of bounded varying delays. Finally, two numerical examples are given to verify the effectiveness of the proposed distributed consensus algorithm

Distributed Tracking Control for Discrete-Time Multiagent Systems with Novel Markovian Switching Topologies

Distributed discrete-time coordinated tracking control problem is investigated for multiagent systems in the ideal case, where agents with a fixed graph combine with a leader-following group, aiming to expand the function of the traditional one in some scenes. The modified union switching topology is derived from a set of Markov chains to the edges by introducing a novel mapping. The issue on how to guarantee all the agents tracking the leader is solved through a PD-like consensus algorithm. The available sampling period and the feasible control gain are calculated in terms of the trigonometric function theory, and the mean-square bound of tracking errors is provided finally. Simulation example is presented to demonstrate the validity of the theoretical results

Consensus Tracking and Containment in Multiagent Networks With State Constraints

The ability of tracking is an important prerequisite for multiagent networks to perform collective activities. This article investigates the problem of containment for a weighted multiagent network with continuous-time agents under state constraints. The network is composed of uninformed and informed agents, where the latter receive external inputs. A new general class of distributed nonlinear controllers is designed for accomplishing both containment and consensus tracking, where the state of each agent is required to stay in its desired convex constraint set. We show that, by using matrix analysis, convex analysis, and Lyapunov theory, all agents eventually converge to the convex hull formed by the external inputs while they obey their constraints during the transience. No relationship is assumed between the convex hull and the intersection of all constraint sets. The consensus tracking problem with a single external input is also solved under this framework. As a generalization, we tackle the multiscaled constrained containment problem, where agents can specify their desired buffer zones by either zooming in or zooming out the convex hull. Numerical examples are provided to illustrate the theoretical results