DECENTRALIZED OPTIMAL CONTROL FOR THE MEAN FIELD LQG PROBLEM OF MULTI-AGENT SYSTEMS

This paper investigates the decentralized optimal control of the linear quadratic Gaussian (LQG) problem in discrete-time stochastic multi-agent systems. The state equations of the subsystems are uncoupled and the individual cost function is coupled with the states of other agents. With the help of state aggregation technique and the mean field structure, we get the decentralized optimal controllers that each agent only uses its own state and an iterative function which may be computed off-line for the optimization of the individual cost function and the social cost function respectively. And then, we prove that as the number of subsystems increases to infinite, the losses of the decentralized controllers and the optimal cost function for the two optimal control problems will go to zero due to the approximation in the optimization. At last, an illustrative example is given.

[1]  D. Fudenberg,et al.  The Theory of Learning in Games , 1998 .

[2]  A. Ōkubo,et al.  MODELLING SOCIAL ANIMAL AGGREGATIONS , 1994 .

[3]  Minyi Huang,et al.  Large-Population Cost-Coupled LQG Problems With Nonuniform Agents: Individual-Mass Behavior and Decentralized $\varepsilon$-Nash Equilibria , 2007, IEEE Transactions on Automatic Control.

[4]  Tao Li,et al.  Asymptotically Optimal Decentralized Control for Large Population Stochastic Multiagent Systems , 2008, IEEE Transactions on Automatic Control.

[5]  Peter E. Caines,et al.  Mean Field LQG Control in Leader-Follower Stochastic Multi-Agent Systems: Likelihood Ratio Based Adaptation , 2012, IEEE Transactions on Automatic Control.

[6]  Zbigniew Dziong,et al.  Fair-efficient call admission control policies for broadband networks—a game theoretic framework , 1996, TNET.

[7]  D. Naidu,et al.  Optimal Control Systems , 2018 .

[8]  P. Caines,et al.  Social optima in mean field LQG control: Centralized and decentralized strategies , 2009 .

[9]  Peter E. Caines,et al.  The NCE (Mean Field) Principle With Locality Dependent Cost Interactions , 2010, IEEE Transactions on Automatic Control.

[10]  Eitan Altman,et al.  A survey on networking games in telecommunications , 2006, Comput. Oper. Res..

[11]  N. Harris.  STOCHASTIC CONTROL , 2011 .

[12]  Kevin M. Passino,et al.  Biomimicry of bacterial foraging for distributed optimization and control , 2002 .

[13]  Hongyan Wang,et al.  Social potential fields: A distributed behavioral control for autonomous robots , 1995, Robotics Auton. Syst..

[14]  Chee-Yee Chong,et al.  Sensor networks: evolution, opportunities, and challenges , 2003, Proc. IEEE.

[15]  Lihua Xie,et al.  Network Topology and Communication Data Rate for Consensusability of Discrete-Time Multi-Agent Systems , 2011, IEEE Transactions on Automatic Control.

[16]  Jing Zhou,et al.  Finite horizon linear quadratic regulation for linear discrete time-varying systems with single/multiple input delay(s) , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.