A multidimensional comparison theorem for solutions of the Skorokhod problem in a wedge with applications to control of a group of independent identical agents

Author

Anulova, Svetlana

Author_Institution

Inst. for Control Sci., Russian Acad. of Sci., Moscow, Russia

fYear

2010

fDate

15-17 Dec. 2010

Firstpage

4177

Lastpage

4179

Abstract

A problem of controlling a group of independent identical agents is considered. Such problems arise in mathematical economics, in robotics (swarms of mini-robots). The model includes a stochastic component. The general method of the Bellman equation cannot be applied to this problem. The solution is found by the comparison method for solutions of stochastic differential equations using the technique of the Skorokhod reflection operators. The optimal policy admits a realization as a decentralized group control algorithm.

Keywords

decentralised control; differential equations; economics; mathematical operators; multi-robot systems; optimal control; realisation theory; stochastic processes; Skorokhod problem; Skorokhod reflection operator; decentralized group control; independent identical agents; mathematical economics; minirobot swarm; multidimensional comparison theorem; optimal policy; realization; robotics; stochastic component; stochastic differential equation; wedge; Differential equations; Economics; Equations; Friction; Mathematical model; Optimal control; Trajectory;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control (CDC), 2010 49th IEEE Conference on

Conference_Location

Atlanta, GA

ISSN

0743-1546

Print_ISBN

978-1-4244-7745-6

Type

conf

DOI

10.1109/CDC.2010.5717401

Filename

5717401