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

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.