Distributed estimation of multi-agent systems with coupling in the measurements: Bulk algorithm and approximate Kalman-type filtering

We consider distributed estimation of a class of large population multi-agent systems where the agents have linear stochastic dynamics and are coupled via their partial observations. The measurements interference model is assumed to depend only on the empirical mean of agents states. In addition, a structural assumption is made on the agents' controls which are constrained to be linear constant feedbacks on a locally based state estimate. In previous work [19], we solved precisely the decentralized optimal estimation problem for a finite population of agents. In particular, we developed a non-sequential bulk estimation algorithm whereby at every time step, all past and present available measurements are considered. In this paper, a Kalman-type recursive approximate filtering approach using exchangeability arguments is presented and tested numerically.

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

[2]  Pravin Varaiya,et al.  Stochastic Systems: Estimation, Identification, and Adaptive Control , 1986 .

[3]  Sean P. Meyn,et al.  A mean-field control-oriented approach to particle filtering , 2011, Proceedings of the 2011 American Control Conference.

[4]  Dirk Helbing,et al.  Simulating dynamical features of escape panic , 2000, Nature.

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

[6]  S. Meyn,et al.  Synchronization of coupled oscillators is a game , 2010, ACC 2010.

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

[8]  Roland P. Malhamé,et al.  Decentralized estimation in a class of measurements induced mean field control problems , 2013, 52nd IEEE Conference on Decision and Control.

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

[10]  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.

[11]  Sean P. Meyn,et al.  Feedback particle filter with mean-field coupling , 2011, IEEE Conference on Decision and Control and European Control Conference.

[12]  Aimé Lachapelle,et al.  Human Crowds and Groups Interactions: a Mean Field Games Approach , 2010 .

[13]  H. Witsenhausen.  A Counterexample in Stochastic Optimum Control , 1968 .

[14]  Arunabha Bagchi.  Optimal Control of Stochastic Systems , 1993 .

[15]  Peter E. Caines,et al.  Distributed Multi-Agent Decision-Making with Partial Observations: Asymtotic Nash Equilibria , 2006 .

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

[17]  Roland P. Malhamé,et al.  Distributed estimation and control for large population stochastic multi-agent systems with coupling in the measurements , 2013, 2013 European Control Conference (ECC).

[18]  Peter E. Caines,et al.  Uplink power adjustment in wireless communication systems: a stochastic control analysis , 2004, IEEE Transactions on Automatic Control.

[19]  P. Lions,et al.  Mean field games , 2007 .

[20]  Peter E. Caines,et al.  Social Optima in Mean Field LQG Control: Centralized and Decentralized Strategies , 2012, IEEE Transactions on Automatic Control.