Moment specification algorithm for control of nonlinear systems driven by Gaussian white noise

Covariance control methods have been applied to linear stochastic multivariable control systems to ensure good behavior of each state variable separately. Recent attempts to extend these ideas to nonlinear systems have been reported, including an example of a system exhibiting hysteresis nonlinearity which employed describing functions. As nonlinearities, including hysteresis, occur frequently in structural systems, the development of effective control algorithms to accommodate them is desirable. Recently, the authors designed covariance controllers for several hysteretic systems using the method of stochastic equivalent linearization. Performance of the closed loop system employing the covariance control was verified through simulation. In the present work, a new control design method is adopted that uses the principle of maximum entropy, which has been used as an alternative procedure for closure of moment equations arising in stochastic dynamical systems. The maximum entropy-based method leads to a result equivalent to that of stochastic linearization when covariances alone are specified; however, the method readily accommodates the specification of higher order response moments.