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# Communications in Information and Systems

## Volume 15 (2015)

### Number 1

### A mean-variance control framework for platoon control problems: Weak convergence results and applications on reduction of complexity

Pages: 57 – 86

DOI: http://dx.doi.org/10.4310/CIS.2015.v15.n1.a5

#### Authors

#### Abstract

This paper introduces a new approach of treating platoon systems using mean-variance 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 represented by stochastic differential equations driven by a Brownian motion. The state space of the Markov chain is large in our setup, which renders practically infeasible for a straightforward implementation of the mean-variance control strategy obtained in the literature. By partitioning the states of the Markov chain into sub-groups (or clusters) and then aggregating the states of each cluster as a super state, we are able to obtain a limit system of much reduced complexity. The justification of the limit system is rigorously supported by establishing certain weak convergence results.

#### Keywords

platoon control, mean-variance control, two-time-scale model, weak convergence, reduction of complexity