Near-Optimal Controls of Differential Systems with Switching and Random Jumps Subject to Fast Switching and Wideband Noise Perturbation

This work develops near-optimal controls for systems given by differential equations with wideband noise and random switching.The random switching is modeled by a continuous-time,time-inhomogeneous Markov chain.Under broad conditions,it is shown that there is an associated limit problem,which is a s...

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Bibliographic Details
Published inActa Mathematicae Applicatae Sinica Vol. 32; no. 1; pp. 17 - 34
Main Authors Yin, G., Guo, Xian-ping, Talafha, Yousef, Baran, Nicholas A.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2016
Subjects
Applications of Mathematics
Math Applications in Computer Science
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
切换
宽带噪声
微分方程组
微分系统
扰动
最优控制
连续时间
马尔可夫链
regime switching
martingale problem
nearoptimal control
wideband noise
05B15
jump diffusion
relaxed control
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ISSN0168-9673
1618-3932
DOI10.1007/s10255-016-0550-4

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Summary:This work develops near-optimal controls for systems given by differential equations with wideband noise and random switching.The random switching is modeled by a continuous-time,time-inhomogeneous Markov chain.Under broad conditions,it is shown that there is an associated limit problem,which is a switching jump diffusion.Using near-optimal controls of the limit system,we then build controls for the original systems.It is shown that such constructed controls are nearly optimal.
Bibliography:11-2041/O1
This work develops near-optimal controls for systems given by differential equations with wideband noise and random switching.The random switching is modeled by a continuous-time,time-inhomogeneous Markov chain.Under broad conditions,it is shown that there is an associated limit problem,which is a switching jump diffusion.Using near-optimal controls of the limit system,we then build controls for the original systems.It is shown that such constructed controls are nearly optimal.
regime switching jump diffusion wideband noise martingale problem relaxed control near-optimal control
ISSN:0168-9673
1618-3932
DOI:10.1007/s10255-016-0550-4