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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| Published in | IEEE transactions on automatic control Vol. 57; no. 4; pp. 904 - 919 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
New York, NY
IEEE
01.04.2012
Institute of Electrical and Electronics Engineers |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0018-9286 1558-2523 1558-2523 |
| DOI | 10.1109/TAC.2011.2174678 |
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| Abstract | 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. |
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| AbstractList | 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. We consider the problem of distributed convergenceto a Nash equilibrium in a noncooperative game where the playersgenerate their actions based only on online measurements oftheir individual cost functions, corrupted with additive measurementnoise. Exact analytical forms and/or parameters ofthe cost functions, as well as the current actions of the playersmay be unknown. Additionally, the players’ actions are subjectto linear dynamic constraints. We propose an algorithm basedon discrete-time stochastic extremum seeking using sinusoidalperturbations and prove its almost sure convergence to a Nashequilibrium. We show how the proposed algorithm can be appliedto solving coordination problems in mobile sensor networks,where motion dynamics of the players can be modeled as: 1) singleintegrators (velocity-actuated vehicles), 2) double integrators(force-actuated vehicles), and 3) unicycles (a kinematic modelwith nonholonomic constraints). Examples are given in which thecost functions are selected such that the problems of connectivitycontrol, formation control, rendezvous and coverage control aresolved in an adaptive and distributed way. The methodology isillustrated through simulations. |
| Author | Johansson, K. H. Stipanovic, D. M. Stankovic, M. S. |
| Author_xml | – sequence: 1 givenname: M. S. surname: Stankovic fullname: Stankovic, M. S. email: milsta@kth.se organization: ACCESS Linnaeus Center, KTH R. Inst. of Technol., Stockholm, Sweden – sequence: 2 givenname: K. H. surname: Johansson fullname: Johansson, K. H. email: kallej@kth.se organization: ACCESS Linnaeus Center, KTH R. Inst. of Technol., Stockholm, Sweden – sequence: 3 givenname: D. M. surname: Stipanovic fullname: Stipanovic, D. M. email: dusan@illinois.edu organization: Dept. of Ind. & Enterprise Syst. Eng., Univ. of Illinois at Urbana-Champaign, Urbana, IL, USA |
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| Keywords | 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 |
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| Snippet | 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... We consider the problem of distributed convergenceto a Nash equilibrium in a noncooperative game where the playersgenerate their actions based only on online... |
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| SubjectTerms | 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 |
| Title | Distributed Seeking of Nash Equilibria With Applications to Mobile Sensor Networks |
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