Extension of the covariance control principle to nonlinear stochastic systems

An approach for the constrained variance control of nonlinear stochastic systems, which uses the theory of covariance control of linear stochastic systems, is proposed. The nonlinear stochastic systems are linearised by the use of describing functions. Two cases of nonlinear systems are considered: zero-mean nonlinear stochastic systems and nonzero-mean nonlinear stochastic systems. The application of this approach to a position servomechanism is illustrated by a numerical example