Dynamics over Signed Networks

A signed network is a network with each link associated with a positive or negative sign. Models for nodes interacting over such signed networks, where two different types of interactions take place along the positive and negative links, respectively, arise from various biological, social, political, and economic systems. As modifications to the conventional DeGroot dynamics for positive links, two basic types of negative interactions along negative links, namely the opposing rule and the repelling rule, have been proposed and studied in the literature. This paper reviews a few fundamental convergence results for such dynamics over deterministic or random signed networks under a unified algebraic-graphical method. We show that a systematic tool of studying node state evolution over signed networks can be obtained utilizing generalized Perron-Frobenius theory, graph theory, and elementary algebraic recursions.Comment: In press, SIAM Revie

Consensus and influence power approximation in time-varying and directed networks subject to perturbations

International audienceThe paper focuses on the analysis of multi-agent systems interacting over directed and time-varying networks in presence of parametric uncertainty on the interaction weights. We assume that agents reach a consensus and the main goal of this work is to characterize the contribution that each agent has to the consensus value. This information is important for network intervention applications such as targeted advertising over social networks. Indeed, for an advertising campaign to be efficient, it has to take into account the influence power of each agent in the graph (i.e., the contribution of each agent to the final consensus value). In our first results we analytically describe the trajectory of the overall network and we provide lower and upper bounds on the corresponding consensus value. We show that under appropriate assumptions, the contribution of each agent to the consensus value is smooth both in time and in the variation of the uncertainty parameter. This allows approximating the contribution of each agent when small perturbations affect the influence of each agent on its neighbors. Finally, we provide a numerical example to illustrate how our theoretical results apply in the context of network intervention

Delay Robustness of Consensus Algorithms: Continuous-Time Theory

Consensus among autonomous agents is a key problem in multiagent control. In this article, we consider averaging consensus policies over time-varying graphs in presence of unknown but bounded communication delays. It is known that consensus is established (no matter how large the delays are) if the graph is periodically, or uniformly quasi-strongly connected (UQSC). The UQSC condition is often believed to be the weakest sufficient condition under which consensus can be proved. We show that the UQSC condition can actually be substantially relaxed and replaced by a condition that we call aperiodic quasi-strong connectivity, which, in some sense, proves to be very close to the necessary condition (the so-called integral connectivity). Under the assumption of reciprocity of interactions (e.g., for undirected or type-symmetric graphs), a necessary and sufficient condition for consensus in presence of bounded communication delays is established; the relevant results have been previously proved only in the undelayed case

Robust Distributed Stabilization of Interconnected Multiagent Systems

Many large-scale systems can be modeled as groups of individual dynamics, e.g., multi-vehicle systems, as well as interconnected multiagent systems, power systems and biological networks as a few examples. Due to the high-dimension and complexity in configuration of these infrastructures, only a few internal variables of each agent might be measurable and the exact knowledge of the model might be unavailable for the control design purpose. The collective objectives may range from consensus to decoupling, stabilization, reference tracking, and global performance guarantees. Depending on the objectives, the designer may choose agent-level low-dimension or multiagent system-level high-dimension approaches to develop distributed algorithms. With an inappropriately designed algorithm, the effect of modeling uncertainty may propagate over the communication and coupling topologies and degrade the overall performance of the system. We address this problem by proposing single- and multi-layer structures. The former is used for both individual and interconnected multiagent systems. The latter, inspired by cyber-physical systems, is devoted to the interconnected multiagent systems. We focus on developing a single control-theoretic tool to be used for the relative information-based distributed control design purpose for any combinations of the aforementioned configuration, objective, and approach. This systematic framework guarantees robust stability and performance of the closed-loop multiagent systems. We validate these theoretical results through various simulation studies

Adaptive consensus of multi-agents in networks with jointly connected topologies

In this paper, the consensus problem of multi-agent following a leader is studied. An adaptive design method is presented for multi-agent systems with non-identical unknown nonlinear dynamics, and for a leader to be followed that is also nonlinear and unknown. By parameterizations of unknown nonlinear dynamics of all agents, a decentralized adaptive consensus algorithm is proposed in networks with jointly connected topologies by incorporating local consensus errors in addition to relative position feedback. Analysis of stability and parameter convergence of the proposed algorithm are conducted based on algebraic graph theory and Lyapunov theory. Finally, examples are provided to validate the theoretical results.http://www.elsevier.com/locate/automaticahb2016Electrical, Electronic and Computer Engineerin

Adaptive leaderless consensus of agents in jointly connected networks

In this paper, the leaderless consensus problem of multi-agent systems with jointly connected topologies and nonlinear dynamics is considered, in which the nonlinear dynamics are assumed to be non-identical and unknown. The unknown nonlinear dynamics existing in the systems are assumed to be linearly parameterized, and an adaptive design method for leaderless multiagent systems is presented. By just using the relative position information between each agent and its neighbours, a distributed adaptive consensus control algorithm for the considered systems is proposed, in which the network graphs are jointly connected. Both the global uniform asymptotical stability and the global uniform asymptotical parameter convergence analysis of the adaptive control algorithm are carried out by using adaptive control theory, Lyapunov theory and algebraic graph theory. Finally, an example is given to illustrate the validity of our theoretical results.The National Natural Science Foundation (NNSF) of China (61273183, 61374028 and 61304162).http://www.elsevier.com/locate/neucom2018-06-30hb2017Electrical, Electronic and Computer Engineerin

An event-driven approach to control and optimization of multi-agent systems

This dissertation studies the application of several event-driven control schemes in multi-agent systems. First, a new cooperative receding horizon (CRH) controller is designed and applied to a class of maximum reward collection problems. Target rewards are time-variant with finite deadlines and the environment contains uncertainties. The new methodology adapts an event-driven approach by optimizing the control for a planning horizon and updating it for a shorter action horizon. The proposed CRH controller addresses several issues including potential instabilities and oscillations. It also improves the estimated reward-to-go which enhances the overall performance of the controller. The other major contribution is that the originally infinite-dimensional feasible control set is reduced to a finite set at each time step which improves the computational cost of the controller. Second, a new event-driven methodology is studied for trajectory planning in multi-agent systems. A rigorous optimal control solution is employed using numerical solutions which turn out to be computationally infeasible in real time applications. The problem is then parameterized using several families of parametric trajectories. The solution to the parametric optimization relies on an unbiased estimate of the objective function's gradient obtained by the "Infinitesimal Perturbation Analysis" method. The premise of event-driven methods is that the events involved are observable so as to "excite" the underlying event-driven controller. However, it is not always obvious that these events actually take place under every feasible control in which case the controller may be useless. This issue of event excitation, which arises specially in multi-agent systems with a finite number of targets, is studied and addressed by introducing a novel performance measure which generates a potential field over the mission space. The effect of the new performance metric is demonstrated through simulation and analytical results