Partial containment control over signed graphs

In this paper, we deal with the containment control problem in presence of antagonistic interactions. In particular, we focus on the cases in which it is not possible to contain the entire network due to a constrained number of control signals. In this scenario, we study the problem of selecting the nodes where control signals have to be injected to maximize the number of contained nodes. Leveraging graph condensations, we find a suboptimal and computationally efficient solution to this problem, which can be implemented by solving an integer linear problem. The effectiveness of the selection strategy is illustrated through representative simulations.Comment: 6 pages, 3 figures, accepted for presentation at the 2019 European Control Conference (ECC19), Naples, Ital

Bipartite Consensus for a Class of Nonlinear Multi-agent Systems Under Switching Topologies:A Disturbance Observer-Based Approach

This paper considers the leader-following bipartite consensus for a class of nonlinear multi-agent systems (MASs) subject to exogenous disturbances under directed fixed and switching topologies, respectively. Firstly, two new output feedback control protocols involving signs of link weights are introduced based on relative output measurements of neighboring agents. In order to estimate the disturbances produced by an exogenous system, a disturbance observer-based approach is developed. Then, sufficient conditions for leader-following bipartite consensus with directed fixed topologies are derived. Furthermore, by assuming that each switching topology contains a directed spanning tree, it is proved that the leader-following bipartite consensus can be realized with the designed output feedback control protocol if the dwell time is larger than a non-negative threshold. Finally, numerical simulations inspired by a real-world DC motors are provided to illustrate the effectiveness of the proposed controllers

Partial containment control over signed graphs

In this paper, we deal with the containment control problem in presence of antagonistic interactions. In particular, we focus on the cases in which it is not possible to contain the entire network due to a constrained number of control signals. In this scenario, we study the problem of selecting the nodes where control signals have to be injected to maximize the number of contained nodes. Leveraging graph condensations, we find a suboptimal and computationally efficient solution to this problem, which can be implemented by solving an integer linear problem. The effectiveness of the selection strategy is illustrated through representative simulations

Differential Inequalities in Multi-Agent Coordination and Opinion Dynamics Modeling

Distributed algorithms of multi-agent coordination have attracted substantial attention from the research community; the simplest and most thoroughly studied of them are consensus protocols in the form of differential or difference equations over general time-varying weighted graphs. These graphs are usually characterized algebraically by their associated Laplacian matrices. Network algorithms with similar algebraic graph theoretic structures, called being of Laplacian-type in this paper, also arise in other related multi-agent control problems, such as aggregation and containment control, target surrounding, distributed optimization and modeling of opinion evolution in social groups. In spite of their similarities, each of such algorithms has often been studied using separate mathematical techniques. In this paper, a novel approach is offered, allowing a unified and elegant way to examine many Laplacian-type algorithms for multi-agent coordination. This approach is based on the analysis of some differential or difference inequalities that have to be satisfied by the some "outputs" of the agents (e.g. the distances to the desired set in aggregation problems). Although such inequalities may have many unbounded solutions, under natural graphic connectivity conditions all their bounded solutions converge (and even reach consensus), entailing the convergence of the corresponding distributed algorithms. In the theory of differential equations the absence of bounded non-convergent solutions is referred to as the equation's dichotomy. In this paper, we establish the dichotomy criteria of Laplacian-type differential and difference inequalities and show that these criteria enable one to extend a number of recent results, concerned with Laplacian-type algorithms for multi-agent coordination and modeling opinion formation in social groups.Comment: accepted to Automatic