Distributed Seeking of Nash Equilibria With Applications to Mobile Sensor Networks

• Published in: IEEE transactions on automatic control Vol. 57; no. 4; pp. 904 - 919
• Main Authors: Stankovic, M. S., Johansson, K. H., Stipanovic, D. M.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.04.2012; Institute of Electrical and Electronics Engineers
• Subjects: 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
• DOI: 10.1109/TAC.2011.2174678

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.