Optimal Vibration Control of a Class of Nonlinear Stochastic Systems with Markovian Jump

The semi-infinite time optimal control for a class of stochastically excited Markovian jump nonlinear system is investigated. Using stochastic averaging, each form of the system is reduced to a one-dimensional partially averaged Itô equation of total energy. A finite set of coupled dynamical program...

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Bibliographic Details
Published inShock and vibration Vol. 2016; no. 2016; pp. 1 - 9
Main Authors Zhu, W. Q., Pu, D., Hu, R. C., Huan, R. H.
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Publishing Corporation 01.01.2016
John Wiley & Sons, Inc
Hindawi Limited
Subjects
Dynamical systems
Markov processes
Mathematical analysis
Methods
Nonlinear dynamics
Optimization
Programming
Stochasticity
Time optimal control
Vibration control
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Summary:The semi-infinite time optimal control for a class of stochastically excited Markovian jump nonlinear system is investigated. Using stochastic averaging, each form of the system is reduced to a one-dimensional partially averaged Itô equation of total energy. A finite set of coupled dynamical programming equations is then set up based on the stochastic dynamical programming principle and Markovian jump rules, from which the optimal control force is obtained. The stationary response of the optimally controlled system is predicted by solving the Fokker-Planck-Kolmogorov (FPK) equation associated with the fully averaged Itô equation. Two examples are worked out in detail to illustrate the application and effectiveness of the proposed control strategy.
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ISSN:1070-9622
1875-9203
DOI:10.1155/2016/9641075