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

Zhixin Yang (Department of Mathematics, University of Wisconsin, Eau Claire, Wisc., U.S.A.)

G. Yin (Department of Mathematics, Wayne State University, Detroit, Michigan, U.S.A.)

Le Yi Wang (Department of Electrical and Computer Engineering, Wayne State University, Detroit, Michigan, U.S.A.)

Hongwei Zhang (Department of Computer Science, Wayne State University, Detroit, Michigan, U.S.A.)

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

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