Stochastic optimal control of MDOF nonlinear systems under combined harmonic and wide-band noise excitations

A strategy for stochastic optimal control of multi-degrees-of-freedom (MDOF) strongly nonlinear systems under combined harmonic and wide-band noise excitations is proposed. First, a stochastic averaging procedure is developed to obtain the partially averaged Itô stochastic differential equations for...

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Bibliographic Details
Published inNonlinear dynamics Vol. 79; no. 2; pp. 1115 - 1129
Main Authors Hu, R. C., Zhu, W. Q.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.01.2015
Springer Nature B.V
Subjects
Automotive Engineering
Classical Mechanics
Computer simulation
Control
Control systems
Control theory
Differential equations
Duffing oscillators
Dynamical Systems
Economic models
Engineering
Excitation
Harmonics
Mathematical analysis
Mechanical Engineering
Noise
Nonlinear control
Nonlinear dynamics
Nonlinear systems
Optimal control
Optimization
Original Paper
Predictive control
Stochasticity
Strategy
Vibration
Harmonic and wind-band noise excitations
Dynamical programming
Stochastic optimal control
Stochastic averaging
Multi-degrees-of-freedom nonlinear systems
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Summary:A strategy for stochastic optimal control of multi-degrees-of-freedom (MDOF) strongly nonlinear systems under combined harmonic and wide-band noise excitations is proposed. First, a stochastic averaging procedure is developed to obtain the partially averaged Itô stochastic differential equations for weakly controlled strongly nonlinear systems under combined harmonic and wide-band noise excitations. Then, the dynamical programming equation for stochastic optimal control problem is derived and solved to yield the optimal control law. Finally, the responses of optimally controlled MDOF nonlinear systems are predicted by solving the Fokker–Planck–Kolmogorov equation associated with the fully averaged Itô stochastic differential equations. As an example, the stochastic optimal control of two coupled Duffing oscillators under combined harmonic and wide-band noise excitations is worked out in detail to illustrate the strategy. The effectiveness of the proposed control strategy is verified using the results from Monte Carlo simulation.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-014-1727-0