LARGE DEVIATIONS FOR TWO-TIME-SCALE SYSTEMS DRIVEN BY NONHOMOGENEOUS MARKOV CHAINS AND ASSOCIATED OPTIMAL CONTROL PROBLEMS

被引：15

作者：

He, Qi ^{[1
]}

Yin, George ^{[1
]}

Zhang, Qing ^{[2
]}

机构：

[1] Wayne State Univ, Dept Math, Detroit, MI 48202 USA

[2] Univ Georgia, Dept Math, Athens, GA 30602 USA

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2011年 / 49卷 / 04期

基金：

美国国家科学基金会;

关键词：

large deviations; nonhomogeneity; Markov chain; averaging principle; ASYMPTOTIC EVALUATION; PROCESS EXPECTATIONS; LARGE TIME; ADDITIVE PROCESSES; LOWER BOUNDS; FUNCTIONALS;

D O I：

10.1137/100806916

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This work develops large deviations principles for systems driven by continuous-time Markov chains with two time scales and related optimal control problems. A distinct feature of our setup is that the Markov chain under consideration is time dependent or inhomogeneous. The use of two-time-scale formulations stems from the effort of reducing computational complexity in a wide variety of applications in control, optimization, and systems theory. Starting with a rapidly fluctuating Markovian system, under irreducibility conditions, both large deviations upper and lower bounds are established for systems with a fixed terminal time and for time-varying dynamic systems. Then the results are applied to certain dynamic systems and linear quadratic control problems.

引用

页码：1737 / 1765

页数：29

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