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
收藏
页码：1737 / 1765
页数：29
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