Approximation and Mean Field Control of Systems of Large Populations

We deal with a class of discrete-time stochastic controlled systems composed by a large population of N interacting individuals. Given that N is large and the cost function is possibly unbounded, the problem is studied by means of a limit model \(\mathcal {M}\), known as the mean field model, which is obtained as limit as N →∞ of the model \(\mathcal {M}_N\) corresponding to the system of N individuals in combination with an approximate algorithm for the cost function.