Distributed Seeking of Nash Equilibria With Applications to Mobile Sensor Networks

Stanković, Miloš S.; Johansson, Karl Henrik; Stipanović, Dušan M.

doi:10.1109/tac.2011.2174678

Cited by 290 publications

(205 citation statements)

References 41 publications

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“…Application domains are in fact numerous and include power systems [1], [2], demand side management [3], [4], [5], network congestion control [6], [7], social networks [8], [9], consensus and flocking [10], [11], robotic and sensor networks [12], [13].…”

Section: Introductionmentioning

confidence: 99%

Proximal Dynamics in Multiagent Network Games

Grammatico

2018

IEEE Trans. Control Netw. Syst.

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Abstract-We consider dynamics and protocols for agents seeking an equilibrium in a network game with proximal quadratic cost coupling. We adopt an operator theoretic perspective to show global convergence to a network equilibrium, under the assumption of convex cost functions with proximal quadratic couplings, time-invariant and time-varying communication graph along with convex local constraints, and time-invariant communication graph along with convex local constraints and separable convex coupling constraints. We show that proximal dynamics generalize opinion dynamics in social networks and are applicable to distributed tertiary control in power networks. Advantageously, distributed computation and communication setups allow each agent to keep its own data private and exchange information with selected agents only. Typically, in networked multi-agent systems, the state (or decision) variables of each agent evolve as a result of local decision making, e.g. local optimization subject to private constraints, and distributed communication with some other agents, according to a communication graph. It then follows naturally that the aim of the agents is to reach a collective equilibrium state, where no agent can benefit from updating its state variables. I. INTRODUCTIONLiterature overview: In this paper, we study network games with proximal, hence quadratic, cost coupling between neighboring agents, that are related to the literature of distributed multi-agent equilibrium seeking in network games and distributed multi-agent optimization.Network games among agents with convex compact local constraints have been considered in [14] under the assumption of strongly convex quadratic cost functions and time-invariant communication graph; in [15] [16], under the assumption of differentiable cost functions with Lipschitz continuous gradient, strictly monotone pseudo-gradient game mapping (hence strictly convex cost functions), and undirected, possibly time-varying, communication graph. Multi-agent games with convex compact local and also coupling constraints have been considered in [17] under the assumption of strongly convex twice differentiable cost functions with bounded gradients, with strictly increasing congestion cost term.

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Section: Introductionmentioning

confidence: 99%

Proximal Dynamics in Multiagent Network Games

Grammatico

2018

IEEE Trans. Control Netw. Syst.

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“…Power networks [1], [2], [3], demand side management [4], [5], social networks [6], [7], [8], consensus and flocking [9], [10], robotic and sensor networks [11], [12], constitute only some multi-agent application domains of contemporary research interest.…”

Section: Introductionmentioning

confidence: 99%

Linear programs for resource sharing among heterogeneous agents: The effect of random agent arrivals

Falsone

Margellos

Garatti

et al. 2017

2017 IEEE 56th Annual Conference on Decision and Control (CDC)

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Abstract-We consider a multi-agent resource sharing problem that can be represented by a linear program. The amount of resource to be shared is fixed, and each agent adds to the linear cost and constraint a term that depends on some randomly extracted parameters, thus modelling heterogeneity among agents. We study the probability that the arrival of a new agent does not affect the optimal value and the resource share of the other agents, which means that the system cannot accommodate the request of a further agent and has reached its saturation limit. In particular, we determine the maximum number of requests for the shared resource that the system can accommodate in a probabilistic sense. This result is proven by first formulating the dual of the resource sharing linear program, and then showing that this is a random linear program. Using results from the scenario theory for randomized optimization, we bound the probability of constraint violation for the dual optimal solution, and prove that this is equivalent with the primal optimal value and resource share remaining unchanged upon arrival of a new agent. We discuss how this can be thought of as probabilistic sensitivity analysis and offer an interpretation of this setting in an electric vehicle charging control problem.

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“…Different types of ESCs have been proposed during the last years aiming to solve standard optimization problems (Nesić, Tan, Moase, & Manzie, 2010;Tan, Nesić, & Mareels, 2006), as well as to achieve online learning in noncooperative and cooperative games (Frihauf, Krstić, & Başar, 2012;Kvaternik & Pavel, 2012;Stanković, Johansson, & Stipanović, 2000). In recent years, there has been interest to address the problem of extremum seeking with constraints.…”

Section: Introductionmentioning

confidence: 99%