Optimal control of a Duffing oscillator under parametric and external excitations

The present paper deals with investigations of a stochastic model of the Duffing oscillator operating continuously. The standard theory of the optimal stochastic control described in Fleming and Richel (1975) is presented, as well as the application of these concept to the perturbation control techniques suggested by Suhardio et al. (1992). The method presented in this paper is, therefore, a generalization of the method of the development of nonlinear control units into a series, as described for Duffing's deterministic oscillator involving stochastic systems derived by the author and applied in
his master thesis (Nowoświat, 1999). Detailed analysis and numerical calculations have been done using the Runge-Kutta procedures.