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"Multiagent systems Mathematical models."
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Graph theoretic methods in multiagent networks
This accessible book provides an introduction to the analysis and design of dynamic multiagent networks. Such networks are of great interest in a wide range of areas in science and engineering, including: mobile sensor networks, distributed robotics such as formation flying and swarming, quantum networks, networked economics, biological synchronization, and social networks. Focusing on graph theoretic methods for the analysis and synthesis of dynamic multiagent networks, the book presents a powerful new formalism and set of tools for networked systems.
The book's three sections look at foundations, multiagent networks, and networks as systems. The authors give an overview of important ideas from graph theory, followed by a detailed account of the agreement protocol and its various extensions, including the behavior of the protocol over undirected, directed, switching, and random networks. They cover topics such as formation control, coverage, distributed estimation, social networks, and games over networks. And they explore intriguing aspects of viewing networks as systems, by making these networks amenable to control-theoretic analysis and automatic synthesis, by monitoring their dynamic evolution, and by examining higher-order interaction models in terms of simplicial complexes and their applications.
The book will interest graduate students working in systems and control, as well as in computer science and robotics. It will be a standard reference for researchers seeking a self-contained account of system-theoretic aspects of multiagent networks and their wide-ranging applications.
This book has been adopted as a textbook at the following universities:
University of Stuttgart, GermanyRoyal Institute of Technology, SwedenJohannes Kepler University, AustriaGeorgia Tech, USAUniversity of Washington, USAOhio University, USA
eBook
Formation Control of Multi-Agent Systems
A comprehensive guide to formation control of multi-agent systems using rigid graph theory This book is the first to provide a comprehensive and unified treatment of the subject of graph rigidity-based formation control of multi-agent systems.
eBook
A machine learning framework for solving high-dimensional mean field game and mean field control problems
Mean field games (MFG) and mean field control (MFC) are critical classes of multiagent models for the efficient analysis of massive populations of interacting agents. Their areas of application span topics in economics, finance, game theory, industrial engineering, crowd motion, and more. In this paper, we provide a flexible machine learning framework for the numerical solution of potential MFG and MFC models. State-of-the-art numerical methods for solving such problems utilize spatial discretization that leads to a curse of dimensionality. We approximately solve high-dimensional problems by combining Lagrangian and Eulerian viewpoints and leveraging recent advances from machine learning. More precisely, we work with a Lagrangian formulation of the problem and enforce the underlying Hamilton– Jacobi–Bellman (HJB) equation that is derived from the Eulerian formulation. Finally, a tailored neural network parameterization of the MFG/MFC solution helps us avoid any spatial discretization. Our numerical results include the approximate solution of 100-dimensional instances of optimal transport and crowd motion problems on a standard work station and a validation using a Eulerian solver in two dimensions. These results open the door to much-anticipated applications of MFG and MFC models that are beyond reach with existing numerical methods.
Journal Article
Multiagent cooperation and competition with deep reinforcement learning
Evolution of cooperation and competition can appear when multiple adaptive agents share a biological, social, or technological niche. In the present work we study how cooperation and competition emerge between autonomous agents that learn by reinforcement while using only their raw visual input as the state representation. In particular, we extend the Deep Q-Learning framework to multiagent environments to investigate the interaction between two learning agents in the well-known video game Pong. By manipulating the classical rewarding scheme of Pong we show how competitive and collaborative behaviors emerge. We also describe the progression from competitive to collaborative behavior when the incentive to cooperate is increased. Finally we show how learning by playing against another adaptive agent, instead of against a hard-wired algorithm, results in more robust strategies. The present work shows that Deep Q-Networks can become a useful tool for studying decentralized learning of multiagent systems coping with high-dimensional environments.
Journal Article
MCMAS: an open-source model checker for the verification of multi-agent systems
We present MCMAS, a model checker for the verification of multi-agent systems. MCMAS supports efficient symbolic techniques for the verification of multi-agent systems against specifications representing temporal, epistemic and strategic properties. We present the underlying semantics of the specification language supported and the algorithms implemented in MCMAS, including its fairness and counterexample generation features. We provide a detailed description of the implementation. We illustrate its use by discussing a number of examples and evaluate its performance by comparing it against other model checkers for multi-agent systems on a common case study.
Journal Article
Neural parameter calibration for large-scale multiagent models
Computational models have become a powerful tool in the quantitative sciences to understand the behavior of complex systems that evolve in time. However, they often contain a potentially large number of free parameters whose values cannot be obtained from theory but need to be inferred from data. This is especially the case for models in the social sciences, economics, or computational epidemiology. Yet, many current parameter estimation methods are mathematically involved and computationally slow to run. In this paper, we present a computationally simple and fast method to retrieve accurate probability densities for model parameters using neural differential equations. We present a pipeline comprising multiagent models acting as forward solvers for systems of ordinary or stochastic differential equations and a neural network to then extract parameters from the data generated by the model. The two combined create a powerful tool that can quickly estimate densities on model parameters, even for very large systems. We demonstrate the method on synthetic time series data of the SIR model of the spread of infection and perform an in-depth analysis of the Harris–Wilson model of economic activity on a network, representing a nonconvex problem. For the latter, we apply our method both to synthetic data and to data of economic activity across Greater London. We find that our method calibrates the model orders of magnitude more accurately than a previous study of the same dataset using classical techniques, while running between 195 and 390 times faster.
Journal Article
Data-driven consensus control of fully distributed event-triggered multi-agent systems
This study investigates the consensus control issue in discrete-time linear multi-agent systems (MASs) using data-driven control under undirected communication networks. To alleviate the communication burden, an adaptive event-triggered control strategy involving only local information is proposed and a model-based stability condition is derived that guarantees the asymptotic consensus of MASs. Furthermore, a data-based consensus condition for unknown MASs is established by combining a data-based system representation with the model-based stability condition, using only pre-collected noisy input-state data instead of the accurate system information a priori. Specifically, both model-based and data-driven event-triggered controllers can be utilized without requiring any global information. The validity and correctness of the controllers and associated theoretical results are demonstrated via numerical simulations.
Journal Article
An SIR model with viral load-dependent transmission
The viral load is known to be a chief predictor of the risk of transmission of infectious diseases. In this work, we investigate the role of the individuals’ viral load in the disease transmission by proposing a new susceptible-infectious-recovered epidemic model for the densities and mean viral loads of each compartment. To this aim, we formally derive the compartmental model from an appropriate microscopic one. Firstly, we consider a multi-agent system in which individuals are identified by the epidemiological compartment to which they belong and by their viral load. Microscopic rules describe both the switch of compartment and the evolution of the viral load. In particular, in the binary interactions between susceptible and infectious individuals, the probability for the susceptible individual to get infected depends on the viral load of the infectious individual. Then, we implement the prescribed microscopic dynamics in appropriate kinetic equations, from which the macroscopic equations for the densities and viral load momentum of the compartments are eventually derived. In the macroscopic model, the rate of disease transmission turns out to be a function of the mean viral load of the infectious population. We analytically and numerically investigate the case that the transmission rate linearly depends on the viral load, which is compared to the classical case of constant transmission rate. A qualitative analysis is performed based on stability and bifurcation theory. Finally, numerical investigations concerning the model reproduction number and the epidemic dynamics are presented.
Journal Article
SecuredTrust: A Dynamic Trust Computation Model for Secured Communication in Multiagent Systems
Security and privacy issues have become critically important with the fast expansion of multiagent systems. Most network applications such as pervasive computing, grid computing, and P2P networks can be viewed as multiagent systems which are open, anonymous, and dynamic in nature. Such characteristics of multiagent systems introduce vulnerabilities and threats to providing secured communication. One feasible way to minimize the threats is to evaluate the trust and reputation of the interacting agents. Many trust/reputation models have done so, but they fail to properly evaluate trust when malicious agents start to behave in an unpredictable way. Moreover, these models are ineffective in providing quick response to a malicious agent's oscillating behavior. Another aspect of multiagent systems which is becoming critical for sustaining good service quality is the even distribution of workload among service providing agents. Most trust/reputation models have not yet addressed this issue. So, to cope with the strategically altering behavior of malicious agents and to distribute workload as evenly as possible among service providers; we present in this paper a dynamic trust computation model called \"SecuredTrust.\" In this paper, we first analyze the different factors related to evaluating the trust of an agent and then propose a comprehensive quantitative model for measuring such trust. We also propose a novel load-balancing algorithm based on the different factors defined in our model. Simulation results indicate that our model compared to other existing models can effectively cope with strategic behavioral change of malicious agents and at the same time efficiently distribute workload among the service providing agents under stable condition.
Journal Article