A given region in 2-D Euclidean space is divided by a unknown linear classifier in to two sets each carrying a label. An agent with known dynamics traversing the given region is able to measure the true label perfectly at its position. By following a trajectory, the agent collects data points comprising of its true position and the label at that position. The objective of the agent is to plan a trajectory across the given region to identify the true classifier with high accuracy while minimizing the control cost across the trajectory. We present the following: (i) the classifier identification problem formulated as a control problem; (ii) geometric interpretation of the control problem resulting in one step modified control problems; (iii) control algorithm that results in a data set which is used to identify the true classifier with high accuracy; (iv) convergence of estimated classifier to the true classifier when observed label is not corrupted by noise; (iv) numerical example demonstrating the utility of the control algorithm.