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In this paper the intrinsic complex nature of engineering systems under control is treated by introducing an approach based on Controlled Stochastic Differential Equations with Markovian Switchings (in short CSDEMS). Technical conditions for the existence and uniqueness of the solutions of the CSDEMS are provided. In this context it is not unusual to deal with non-linear CSDEMS that cannot be solved analytically. Therefore, we develop a new two-step, predictor-corrector method for finding numerical approximations to solutions of CSDEMS. This method utilizes the Euler-Maruyama method. An illustrative application to the biochemical engineering area is presented to highlight the usefulness of our approach as a simulation tool.