Application of statistical linearization techniques to design of quasi-optimal active control of nonlinear systems

A comparison between the applicability of statistical linearization methods with moment criteria and criteria in probability density space to the determination of quasi-optimal external control for the nonlinear dynamic system excited by a coloured Gaussian noise and the mean square criterion is discussed in this paper. To determine the quasi-optimal control two modified versions of a standard iterative procedure are proposed, where three versions of statistical linearization with moment criteria and two versions with criteria in the probability density space were combined with the optimal control method for linear systems with the mean square criterion. The detailed considerations are given for a nonlinear 2-degree-of-freedom system with external control force excited by a coloured Gaussian noise which is reated as an output of 2D linear filter. The control is assumed as a linear feedback. The obtained results are illustrated by a numerical example.