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

Author:

Hu Rongchun1,Lü Qiangfeng2

Affiliation:

1. Department of Engineering Mechanics, MIIT Key Laboratory of Dynamics and Control of Complex Systems, Northwestern Polytechnical University, Xi’an 710129, P. R. China

2. Department of Mechanics, State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou, 310027, P. R. China

Abstract

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Mechanical Engineering,Ocean Engineering,Aerospace Engineering,Building and Construction,Civil and Structural Engineering

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