Response of nonlinear systems in probability domain using stochastic averaging

2007 ◽  
Vol 302 (1-2) ◽  
pp. 152-166 ◽  
Author(s):  
Deepak Kumar ◽  
T.K. Datta
Keyword(s):  
Nonlinear Systems ◽  
Stochastic Averaging ◽  
Probability Domain

A Stochastic Averaging Approach for Feedback Control Design of Nonlinear Systems Under Random Excitations

2002 ◽  
Vol 124 (4) ◽  
pp. 561-565 ◽  
Author(s):  
O. Elbeyli ◽  
J. Q. Sun
Keyword(s):  
Feedback Control ◽  
Nonlinear Systems ◽  
Control Design ◽  
Stochastic Averaging ◽  
Moment Equation ◽  
Design Criteria ◽  
Numerical Examples ◽  
Rayleigh Approximation ◽  
Stochastic Controls ◽  
The Moment

This paper presents a method for designing and quantifying the performance of feedback stochastic controls for nonlinear systems. The design makes use of the method of stochastic averaging to reduce the dimension of the state space and to derive the Ito^ stochastic differential equation for the response amplitude process. The moment equation of the amplitude process closed by the Rayleigh approximation is used as a means to characterize the transient performance of the feedback control. The steady state and transient response of the amplitude process are used as the design criteria for choosing the feedback control gains. Numerical examples are studied to demonstrate the performance of the control.

scholarly journals The influence of nonlinear terms in mechanical systems having two degrees of freedom

2006 ◽  
Vol 28 (3) ◽  
pp. 155-164
Author(s):  
Nguyen Duc Tinh
Keyword(s):  
Nonlinear Systems ◽  
White Noise ◽  
Degrees Of Freedom ◽  
Averaging Method ◽  
Duffing Oscillator ◽  
Stochastic Averaging ◽  
Stochastic Averaging Method ◽  
Higher Order ◽  
White Noise Excitation ◽  
Two Degree Of Freedom

For many years the higher order stochastic averaging method has been widely used for investigating nonlinear systems subject to white and coloured noises to predict approximately the response of the systems. In the paper the method is further developed for two-degree-of-freedom systems subjected to white noise excitation. Application to Duffing oscillator is considered.

Optimal Time-Delay Control for Multi-Degree-of-Freedom Nonlinear Systems Excited by Harmonic and Wide-Band Noises

2021 ◽  
pp. 2150053
Author(s):  
Rongchun Hu ◽  
Qiangfeng Lü
Keyword(s):  
Time Delay ◽  
Nonlinear Systems ◽  
Control Strategy ◽  
Wide Band ◽  
Stochastic Averaging ◽  
Degree Of Freedom ◽  
Optimal Time ◽  
Time Delay Control ◽  
Strongly Nonlinear ◽  
Delay Control

In this paper, an optimal time-delay control strategy is designed for multi-degree-of-freedom (multi-DOF) strongly nonlinear systems excited by harmonic and wide-band noises. First, by using the generalized harmonic functions, a stochastic averaging method (SAM) is employed for the time-delay controlled strongly nonlinear system under combined harmonic and wide-band noise excitations, by which a set of partially averaged Itô equations are obtained. Then, by solving the dynamical programming equation associated with the partially averaged Itô equations, the optimal control law can be obtained. Finally, by solving the Fokker–Planck–Kolmogorov (FPK) equation, the responses of the optimally time-delay controlled system are predicted. The analytical results are compared with the Monte Carlo simulation to verify the effectiveness and efficiency of the proposed control strategy.

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