Optimal polynomial control of nonlinear stochastic dynamical systems.

According to the principle of physical stochastic optimal control, a novel stochastic optimal control strategy is developed in the context of optimal polynomial control that is well-adapted to nonlinear stochastic dynamical systems. Duffing oscillators with varying levels of nonlinearity, subjected to random ground motions, are investigated for illustrative purposes. Numerical results indicate that the statistical variability of system responses gains an obvious reduction, and the system performance improves significantly after the optimal polynomial controller is mounted. Using the control criterion with the minimum of the exceedance probability of system quantities in energy trade-off sense, the lst-order controller suffices even for strongly nonlinear systems. This bypasses the need to utilize nonlinear controllers which may be associated with dynamical instabilities due to time delay and computational dynamics. Besides, the optimal polynomial controller exhibits high robustness to the levels of nonlinearity of Duffing oscillators. The classical statistical linearization based LQG, however, using the nominal Gaussian white noise as the external excitation does not have this advantage. [ABSTRACT FROM AUTHOR]