NONLINEAR OPTIMAL CONTROL OF RANDOMLY BASE-EXCITED DUFFING OSCILLATORS

摘要

A non-linear optimal control strategy for randomly base-excited Duffing oscillators is developed in the context of physical stochastic optimal control of structures by integrating the classical scheme of optimal polynomial control. A family of hardening Duffing oscillators with varying levels of nonlinearities is investigated for illustrative purposes. Numerical results indicate that the statistical variability of system responses gains an obvious reduction,and the system performance improves significantly employing the designed polynomial controller. Using the control criterion,meanwhile,with the minimum of the exceedance probability of system quantities in energy trade-off sense,a lst-order controller suffices even for strongly nonlinear systems. This bypasses the need to utilize non-linear controllers which may be associated with dynamical instabilities due to time delay and computational dynamics.