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Shock and Vibration
Volume 2016, Article ID 9641075, 9 pages
Research Article

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

Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, China

Received 15 May 2015; Accepted 26 August 2015

Academic Editor: Mickaël Lallart

Copyright © 2016 R. H. Huan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.