A class of optimal control problems with N agents where the agents have nonlinear dynamics, nonlinear cost functions and have mean field coupling in their cost functions are considered. The basic objective of the agents is to minimize a social cost which is the sum of the N individual cost functions. The exact socially optimal control policies require a centralized information structures for each agent and have high implementation complexity. Considering the mean field coupling in the cost functions and motivated by the analysis in mean field game theory, a decentralized cooperative optimization problem is formulated where each agent's control policy only depends on its own state and a function which may be computed offline. It is shown that the resulting set of strategies asymptotically achieves person-by-person optimality as N → ∞ where the essential idea is to formulate an (inverse) control problem which yields an optimum solution to the variation in the social cost that occurs due to the variation in an individual agent's control law.

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Persistent URL dx.doi.org/10.1109/CDC.2016.7799199
Conference 55th IEEE Conference on Decision and Control, CDC 2016
Sen, N. (Nevroz), Huang, M, & Malhame, R.P. (Roland P.). (2016). Mean field social control with decentralized strategies and optimality characterization. In 2016 IEEE 55th Conference on Decision and Control, CDC 2016 (pp. 6056–6061). doi:10.1109/CDC.2016.7799199