Distributed extremum seeking for real-time resource allocation

In this paper we present a distributed extremum seeking control, designed to perform real-time resource allocation in multi-agent systems (MAS). The algorithm allows the optimal allocation of a given resource, in a distributed architecture, where each agent shares information only with its neighboring agents, and needs to only measure its own individual payoff function. We combine ideas from recent evolutionary game theory dynamics and the classic extremum seeking control to ensure convergence to an optimal allocation. The application of the algorithm is illustrated via simulation.

[1]  Ying Tan,et al.  ON NON-LOCAL STABILITY PROPERTIES OF EXTREMUM SEEKING CONTROL , 2005 .

[2]  M. Pachter,et al.  Lyapunov stability theory , 1980 .

[3]  Tim Roughgarden,et al.  Generalized Efficiency Bounds in Distributed Resource Allocation , 2014, IEEE Trans. Autom. Control..

[4]  Toshihide Ibaraki,et al.  Resource allocation problems - algorithmic approaches , 1988, MIT Press series in the foundations of computing.

[5]  Andres Pantoja,et al.  Dispatch of distributed generators using a local replicator equation , 2011, IEEE Conference on Decision and Control and European Control Conference.

[6]  Ying Tan,et al.  A unifying approach to extremum seeking: Adaptive schemes based on estimation of derivatives , 2010, 49th IEEE Conference on Decision and Control (CDC).

[7]  Nicanor Quijano,et al.  A Shahshahani Gradient based extremum seeking scheme , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[8]  Miroslav Krstic,et al.  Multi-agent deployment in the plane using stochastic extremum seeking , 2010, 49th IEEE Conference on Decision and Control (CDC).

[9]  Asuman E. Ozdaglar,et al.  Distributed Subgradient Methods for Multi-Agent Optimization , 2009, IEEE Transactions on Automatic Control.

[10]  B. Paden,et al.  Lyapunov stability theory of nonsmooth systems , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[11]  Ying Tan,et al.  A unifying framework for analysis and design of extremum seeking controllers , 2012, 2012 24th Chinese Control and Decision Conference (CCDC).

[12]  Prashant J. Shenoy,et al.  Resource management for real-time tasks in mobile robotics , 2007, J. Syst. Softw..

[13]  Nicanor Quijano,et al.  Dynamic bandwidth allocation in wireless networks using a Shahshahani gradient based extremum seeking control , 2012, 2012 6th International Conference on Network Games, Control and Optimization (NetGCooP).

[14]  Zhimei Jiang,et al.  Channel quality dependent scheduling for flexible wireless resource management , 2001, GLOBECOM'01. IEEE Global Telecommunications Conference (Cat. No.01CH37270).

[15]  Miroslav Krstic,et al.  Stability of extremum seeking feedback for general nonlinear dynamic systems , 2000, Autom..

[16]  Josef Hofbauer,et al.  Evolutionary Games and Population Dynamics , 1998 .

[17]  Naoki Katoh,et al.  Resource Allocation Problems , 1998 .

[18]  Miroslav Krstic,et al.  Real-Time Optimization by Extremum-Seeking Control: Ariyur/Extremum Seeking , 2004 .

[19]  Viktor K. Prasanna,et al.  MIP formulation for robust resource allocation in dynamic real-time systems , 2005, J. Syst. Softw..

[20]  E. Akin.  The Differential Geometry of Population Genetics and Evolutionary Games , 1990 .

[21]  Günther Palm,et al.  Evolutionary stable strategies and game dynamics for n-person games , 1984 .

[22]  M. Krstić,et al.  Real-Time Optimization by Extremum-Seeking Control , 2003 .

[23]  N Ghods,et al.  Multi-agent deployment around a source in one dimension by extremum seeking , 2010, Proceedings of the 2010 American Control Conference.

[24]  Bruno Sinopoli,et al.  Dynamic power allocation in server farms: A Real Time Optimization approach , 2010, 49th IEEE Conference on Decision and Control (CDC).

[25]  Frank Kelly,et al.  Charging and rate control for elastic traffic , 1997, Eur. Trans. Telecommun..

[26]  Milos S. Stankovic,et al.  Distributed seeking of Nash equilibria in mobile sensor networks , 2010, 49th IEEE Conference on Decision and Control (CDC).

[27]  Daniel Pérez Palomar,et al.  A tutorial on decomposition methods for network utility maximization , 2006, IEEE Journal on Selected Areas in Communications.