This paper investigates the charging control strategy design problem of a large-scale plug-in electric vehicle (PEV) group, where each PEV aims to find an optimal charging strategy to minimize its own cost function. It should be noted that the collective behavior of the group is coupled in the individual cost function, which complicates the design of decentralized charging strategies. To obtain the decentralized charging strategy, a mean-field game (MFG) formulation is proposed where a penalty on collective consensus is embedded and a class of mean-field coupled time-varying stochastic systems is targeted for solving the MFG which involves the charging model of PEVs as a special case. Then, an augmented system with dimension extension and the policy iteration algorithm are proposed to solve the mean-field game problem for the class of mean-field coupled time-varying stochastic systems. Moreover, analysis of the convergence of proposed approach has been studied. Last, simulation is conducted to illustrate the effectiveness of the proposed MFG-based charging control strategy and shows that the charging control strategy can achieve desired mean-field state and impact to the power grid can be buffered.

Quad-core cpus have been a common desktop configuration for today's office. The increasing number of processors on a single chip opens new opportunity for parallel computing. Our goal is to make use of the multi-core as well as multi-processor architectures to speed up large-scale data mining algorithms. In this paper, we present a general parallel learning framework, Cut-And-Stitch, for training hidden Markov chain models. Particularly, we propose two model-specific variants, CAS-LDS for learning linear dynamical systems (LDS) and CAS-HMM for learning hidden Markov models (HMM). Our main contribution is a novel method to handle the data dependencies due to the chain structure of hidden variables, so as to parallelize the EM-based parameter learning algorithm. We implement CAS-LDS and CAS-HMM using OpenMP on two supercomputers and a quad-core commercial desktop. The experimental results show that parallel algorithms using Cut-And-Stitch achieve comparable accuracy and almost linear speedups over the traditional serial version.