Probability-Weighted Optimal Control for Nonlinear Stochastic Vibrating Systems with Random Time Delay

A probability-weighted optimal control strategy for nonlinear stochastic vibrating systems with random time delay is proposed. First, by modeling the random delay as a finite state Markov process, the optimal control problem is converted into the one of Markov jump systems with finite mode. Then, up...

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Bibliographic Details
Published inShock and vibration Vol. 2018; no. 2018; pp. 1 - 8
Main Authors Ying, Z. G., Wang, X. F., Lü, Q. F., Hu, R. C., Huan, R. H.
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Publishing Corporation 01.01.2018
Hindawi
John Wiley & Sons, Inc
Hindawi Limited
Subjects
Communications networks
Control systems
Delay
Markov analysis
Markov chains
Mathematical problems
Mechanics
Nonlinear control
Nonlinear systems
Optimal control
Probability distribution
Probability theory
System theory
Time lag
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Summary:A probability-weighted optimal control strategy for nonlinear stochastic vibrating systems with random time delay is proposed. First, by modeling the random delay as a finite state Markov process, the optimal control problem is converted into the one of Markov jump systems with finite mode. Then, upon limiting averaging principle, the optimal control force is approximately expressed as probability-weighted summation of the control force associated with different modes of the system. Then, by using the stochastic averaging method and the dynamical programming principle, the control force for each mode can be readily obtained. To illustrate the effectiveness of the proposed control, the stochastic optimal control of a two degree-of-freedom nonlinear stochastic system with random time delay is worked out as an example.
ISSN:1070-9622
1875-9203
DOI:10.1155/2018/5636541