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

Zhixin Yang; G. Yin; Le Yi Wang; Hongwei Zhang

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arXiv · 1401.5058

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

Zhixin Yang·G. Yin·Le Yi Wang·Hongwei Zhang

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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 given 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 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.

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BibTeX RIS

Zhixin Yang, G. Yin, Le Yi Wang, Hongwei Zhang. 2014-01-17. A Mean-Variance Control Framework for Platoon Control Problems: Weak Convergence Results and Applications on Reduction of Complexity. https://arxiv.org/abs/1401.5058

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