A Mean-Variance Control Framework for Platoon Control Problems: Weak Convergence Results and Applications on Reduction of Complexity

This paper is concerned with a new angle of treating platoon systems using meanvariance control formulation. The underlying system is a controlled switching diffusion in which the random switching process is a continuous-time Markov chain. This switching process is used to represent random environment and other random factors that cannot be given by stochastic differential equations driven by a Brownian motion. The state space of the Markov chain is large in our setup, which renders a straightforward implementation of the mean-variance control strategy obtained in the literature practically unfeasible. By noting that the states of the Markov chain can be split into sub-groups (or clusters) and then by aggregating states of each cluster as a super state, we are able to obtain a limit system. The justification of the limit system is rigorously done by obtaining certain weak convergence results. This research was supported in part by the National Science Foundation under CNS-1136007. Department of Mathematics, Wayne State University, Detroit, Michigan 48202, [email protected]. Department of Mathematics, Wayne State University, Detroit, Michigan 48202, [email protected]. Department of Electrical and Computer Engineering, Wayne State University, Detroit, MI 48202, [email protected]. Department of Computer Science, Wayne State University, Detroit, MI 48202, [email protected]. 1