Humans can often conduct both linear and nonlinear control tasks after a sufficient number of trials, even if they initially do not have sufficient knowledge about the system's dynamics and the way to control it. Theoretically, it is well known that some nonlinear systems cannot be stabilized asymptotically by any linear controllers. However, such differences between linear and nonlinear controls from the viewpoint of brain activities are still unclear. In this paper, we have conducted an f-MRI experiment using complex nonlinear control tasks where subjects are required to control a 2-link planer under actuated manipulator (2PUAM). The 2PUAM has nonholonomic constrains and cannot be stabilized asymptotically by any linear controller. Although there are similar activations such as in motor cortex and somatosensory cortex, some differences between linear and nonlinear cases have been observed by the f-MRI. According to the brain function mapping, the result implies that some additional information such as the shape of the manipulator and its trajectory, which are not needed for linear control tasks, may be required to control the 2PUAM. Therefore, this suggests that the difference in linear and nonlinear control tasks can be observed through the brain activities.