Nash, Social and Centralized Solutions to Consensus Problems via Mean Field Control Theory

Nourian, Mojtaba; Caines, Peter E.; Malhamé, Roland P.; Huang, Minyi

doi:10.1109/tac.2012.2215399

Cited by 93 publications

(69 citation statements)

References 30 publications

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“…Note that in (13) and (14), we use θ instead of i to emphasize the point that we have a continuum of agents under the parameter set and its empirical distribution in Assumption 2. Further note that (14) describes the average behavior of all the agents within Θ; hence it must be consistent with the mean field coupling term in (5) when N is sufficiently large.…”

Section: Mean Field Systemmentioning

confidence: 90%

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Discrete-time LQG mean field games with unreliable communication

Moon

Başar

2014

53rd IEEE Conference on Decision and Control

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Abstract-In this paper, we consider discrete-time linearquadratic-Gaussian (LQG) mean field games over unreliable communication links. These are dynamic games with a large number of agents where the cost function of each agent is coupled with other agents' states via a mean field term. Further, the individual dynamical system for each agent is subject to packet dropping. Under this setup, we first obtain an optimal decentralized control law for each agent that is a function of local information as well as packet drop information. We then construct a mean field system that provides the best approximation to the mean field term under appropriate conditions. We also show that the optimal decentralized controller stabilizes the individual dynamical system in the time-average sense. We prove an -Nash equilibrium property of the set of N optimal decentralized controllers, and show that can be made arbitrarily small as the number of agents becomes arbitrarily large. We note that the existence of the -Nash equilibrium obtained in this paper is primarily dependent on the underlying communication networks.

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Section: Mean Field Systemmentioning

confidence: 90%

“…In [12], LQG mean field games with Markov jump parameters were studied. In [13], the mean field adaptive control problem was studied, and the consensus problem was discussed in [14]. Discrete-time mean field games under the notion of oblivious equilibria were discussed in [2], [5].…”

Section: Introductionmentioning

confidence: 99%

Discrete-time LQG mean field games with unreliable communication

Moon

Başar

2014

53rd IEEE Conference on Decision and Control

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“…Consensus in multi agents systems is also defined and studied in fields far away from classical control theory. For example, Games Theoretical approaches [28,37,40] or Max Plus algebra systems [25,26]. Nevertheless, these efforts have still left many unanswered questions.…”

Section: Zusammenfassungmentioning

confidence: 99%

Consensus in Multi‐agent Systems

Wen

Chen

et al. 2016

Distributed Cooperative Control of Multi‐agent Systems

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A Carlos Elías y a Marina. AbstractDuring the last decade, the problem of consensus in multiagents systems has been studied with special emphasis on graph theoretical methods. Consensus can be regarded as a control objective in which is sought that all systems, or agents, in a network have an equivalent output value. This is achieved through a given control strategy usually referred to as consensus algorithm. The motivation to study such an objective comes from different areas, such as engineering, and social and natural sciences. In the control engineering field, important application examples are formation control of swarms of mobile robots and distributed electric generation. Most of the work in this area is done for agents with single or double integrator dynamics and algorithms derived as the Laplacian matrix of undirected graphs. That is, consensus is often studied as a property of particular networks and particular algorithms.In this thesis, we tackle the problem from a Control Theory perspective in an attempt to augment the class of systems that can be studied. For that we translate the consensus problem from its classical formulation for integrator systems into a general continuous time stability problem. From here, different algorithmic strategies under several dynamical assumptions of the agents can be studied through well known control theoretical tools -as Lyapunov's theory, linear matrix inequalities (LMI), or robust control -along with graph theoretical concepts. In particular, in this work we study consensus of agents with arbitrary linear dynamics under the influence of linear algorithms not necessarily derived from graphs. Furthermore, we include the possibility that the agents are disturbed by several factors as external signals, parameter uncertainties, switching dynamics, or communication failure. The theoretical analysis is also applied to the problem of power sharing in electric grids and to the analysis of distributed formation control.

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“…This feature demonstrates the link of SoS to distributed and decentralized control schemes with the additional property that the interaction between the subsystems may indicate a timevarying coupling. It is this special feature that indicates the links to a rather new category of management and control schemes referred to as coalitional management schemes [24]. In this paradigm different agents cooperate when there is enough interaction between the controlled systems and they work in a decentralized fashion when there is little interaction.…”

Section: Coalition Gamesmentioning

confidence: 99%

Systems of Systems: A Control Theoretic View

Karcanias

2013

2013 IEEE International Conference on Systems, Man, and Cybernetics

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This is the accepted version of the paper.This version of the publication may differ from the final published version. Abstract-This paper considers the notion of SoS as an evolution of the standard notion of systems, provides a clear distinction to the standard notion of composite systems and aims to provide an abstract and generic definition that is detached from the particular domain as well as a classification of the families of SoS. We present a new abstract definition of the notion of System of Systems as an evolution of the notion of Composite Systems, empowered by the concept of autonomy and participation in tasks usually linked to games. Control theoretic concepts and methodologies are used to provide the characterization of the notion of "systems play" that is used as the evolution of the notion of the interconnection topology. In this set up the subsystems in SoS act as autonomous intelligent agents in a multi-agent system that is defined by a central task and possibly a game. Permanent

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Nash, Social and Centralized Solutions to Consensus Problems via Mean Field Control Theory

Cited by 93 publications

References 30 publications

Discrete-time LQG mean field games with unreliable communication

Discrete-time LQG mean field games with unreliable communication

Consensus in Multi‐agent Systems

Systems of Systems: A Control Theoretic View

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