A Moment Specification Algorithm for Control of Nonlinear Systems Driven by Gaussian White Noise

Abstract

Covariance control methods have been applied to linearstochastic multivariable control systems to ensure good behavior of eachstate variable separately. Recent attempts to extend these ideas tononlinear systems have been reported, including an example of a systemexhibiting hysteresis nonlinearity which employed describing functions.As nonlinearities, including hysteresis, occur frequently in structuralsystems, the development of effective control algorithms to accommodatethem is desirable. Recently, the authors designed covariance controllersfor several hysteretic systems using the method of stochastic equivalentlinearization. Performance of the closed loop system employing thecovariance control was verified through simulation. In the present work,a new control design method is adopted that uses the principle ofmaximum entropy, which has been used as an alternative procedure forclosure of moment equations arising in stochastic dynamical systems. Themaximum entropy-based method leads to a result equivalent to that ofstochastic linearization when covariances alone are specified; however,the method readily accommodates the specification of higher orderresponse moments.