Modeling and Controls of Large-Scale Switching Diffusion Networks with Mean-Field Interactions

Large-scale and complex stochastic networked systems are common in broad spectra of applications, such as smart grids, finance, social networks, edge/cloud computing, etc. Many of such systems inevitably involve mean-field interactions. It is of essential importance to develop the methods for solving the optimal control problems. In this paper, we first present a number of motivational models and problems. Then we present new approaches for obtaining the maximum principle to treat large-scale switched systems with mean-field interactions. One of the key ideas is to use the conditional mean field. The maximum principle forms a foundation on which we can solve the corresponding LQG (linear quadratic Gaussian) regulation problems. We also consider the case that the modulating Markov chain switches rapidly with weak and strong interactions. In such a case, the discrete part of the state space becomes nearly decomposable. We show the optimal controls can be obtained.