Safe regions with partial control of a chaotic system in the presence of white Gaussian noise

Noise is present in a wide variety of engineering systems, and it can play a significant role in influencing system dynamics. Under the influence of noise, it has been shown that the response of many discrete-time dynamical systems can be moved away from a particular region. In the present study, the partial control scheme constructed for a chaotic system is applied for confining the trajectories inside a particular region despite the presence of white noise. The proposed algorithm is independent of the dimension of the system. As an illustration, the partial control method has been applied to restrict the response of a Duffing oscillator to a certain state-space region. Different noise forms are considered and numerical results are presented to illustrate the effectiveness of this control method.