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Article overview
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Team Optimal Decentralized Control of System with Partially Exchangeable Agents--Part 1: Linear Quadratic Mean-Field Teams | Jalal Arabneydi
; Aditya Mahajan
; | Date: |
1 Sep 2016 | Abstract: | We consider team optimal control of decentralized systems with linear
dynamics and quadratic costs that consist of multiple sub-populations with
exchangeable agents (i.e., exchanging two agents within the same sub-population
does not affect the dynamics or the cost). Such a system is equivalent to one
where the dynamics and costs are coupled across agents through the mean-field
(or empirical mean) of the states and actions. Two information structures are
investigated. In the first, all agents observe their local state and the
mean-field of all sub-populations; in the second, all agents observe their
local state but the mean- field of only a subset of the sub-populations. Both
information structures are non-classical and not partially nested. Nonetheless,
it is shown that linear control strategies are optimal for the first and
approximately optimal for the second; the approximation error is inversely
proportional to the size of the sub-populations whose mean-fields are not
observed. The corresponding gains are determined by the solution of K+1 Riccati
equations, where K is the number of sub-populations. The dimensions of the
Riccati equations do not depend on the size of the sub-populations; thus the
solution complexity is independent of the number of agents. Generalizations to
major-minor agents, tracking cost, weighted mean-field, and infinite horizon
are provided. The results are illustrated using an example of demand response
in smart grids. | Source: | arXiv, 1609.0056 | Services: | Forum | Review | PDF | Favorites |
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