Application of linearization methods with probability density criteria in control problems

The application of statistical and equivalent linearization methods with criteria in probability density space to the determination of quasi-optimal control for the nonlinear dynamic system with the quadratic criterion is discussed in the paper. To determine the quasi-optimal control two modified versions of standard iterative procedure are proposed, where two versions of statistical and equivalent linearization methods were combined with the optimal control method for linear systems with the mean-square criterion. The detailed considerations and numerical results are given for the Duffing oscillator