Distributed Seeking of Nash Equilibria With Applications to Mobile Sensor Networks

We consider the problem of distributed convergence to a Nash equilibrium in a noncooperative game where the players generate their actions based only on online measurements of their individual cost functions, corrupted with additive measurement noise. Exact analytical forms and/or parameters of the...

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Vydáno v:IEEE transactions on automatic control Ročník 57; číslo 4; s. 904 - 919
Hlavní autoři: Stankovic, M. S., Johansson, K. H., Stipanovic, D. M.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York, NY IEEE 01.04.2012
Institute of Electrical and Electronics Engineers
Témata:
Algorithm design and analysis
Applied sciences
Artificial intelligence
Computer science; control theory; systems
Computer systems and distributed systems. User interface
Convergence
Cost function
Exact sciences and technology
extremum seeking
Game theory
Games
Heuristic algorithms
learning
mobile sensor networks
multi-agent control
Nash equilibrium
Noise
noncooperative games
Operational research and scientific management
Operational research. Management science
Software
SRA - ICT
SRA - Informations- och kommunikationsteknik
stochastic optimization
Nash strategy
Extreme search
Nash equilibrium
learning
Fork join problem
Modeling
Adaptive method
Convergence
stochastic optimization
multi-agent control
Non cooperative game
Kinematics
Cost function
Integrator
Game equilibrium
Additive noise
Almost sure convergence
Probabilistic approach
Coordination
Non holonomic system
mobile sensor networks
noncooperative games
Game theory
extremum seeking
Stochastic programming
Multiagent system
Discrete time
Problem solving
Wireless network
Sensor array
Artificial intelligence
Mobile computing
ISSN:0018-9286, 1558-2523, 1558-2523
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Popis
Shrnutí:We consider the problem of distributed convergence to a Nash equilibrium in a noncooperative game where the players generate their actions based only on online measurements of their individual cost functions, corrupted with additive measurement noise. Exact analytical forms and/or parameters of the cost functions, as well as the current actions of the players may be unknown. Additionally, the players' actions are subject to linear dynamic constraints. We propose an algorithm based on discrete-time stochastic extremum seeking using sinusoidal perturbations and prove its almost sure convergence to a Nash equilibrium. We show how the proposed algorithm can be applied to solving coordination problems in mobile sensor networks, where motion dynamics of the players can be modeled as: 1) single integrators (velocity-actuated vehicles), 2) double integrators (force-actuated vehicles), and 3) unicycles (a kinematic model with nonholonomic constraints). Examples are given in which the cost functions are selected such that the problems of connectivity control, formation control, rendezvous and coverage control are solved in an adaptive and distributed way. The methodology is illustrated through simulations.
ISSN:0018-9286
1558-2523
1558-2523
DOI:10.1109/TAC.2011.2174678