OPTIMAL BOUNDED CONTROL OF TRANSIENT RESPONSE OF RAYLEIGH-DUFFING OSCILLATOR UNDER COLORED NOISE EXCITATIONS

The transient response and its optimal bounded control of a Rayleigh-Duffing oscillator driven by colored noises are studied theoretically. The disturbances are assumed to be weak. The standard stochastic averaging method is firstly adopted to obtain the partly averaged It#x000f4; stochastic differential equation for a original system amplitude process. The optimal bounded control algorithm is built by Bellman dynamic programming principle combined with control constraints. Finishing all the averaging procedures, the completed averaged It#x000f4; stochastic differential equation and corresponding Fokker-Planck-Kolmogorov equation are established. Then, the controlled system transient responses are predicted by applying Galerkin method to the obtained Fokker-Planck-Kolmogorov equation. The base functions used in the Galerkin scheme are obtained from a degenerated linear system. Finally, Monte Carlo simulation is used to verify the theoretical results reliability. Calculations show that: 1) the proposed method is effective at solving the transient response of an optimally bounded controlled stochastic nonlinear system; 2) the control algorithm does successfully reduce the transient response of the system; 3) the calculation efficiency of the theoretical method is higher than that of Monte Carlo simulation.