  A given region in 2-D Euclidean space is divided by a unknown linear
classifier in to two sets each carrying a label. The objective of an agent with
known dynamics traversing the region is to identify the true classifier while
paying a control cost across its trajectory. We consider two scenarios: (i) the
agent is able to measure the true label perfectly; (ii) the observed label is
the true label multiplied by noise. 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 algorithms that result in data sets which are
used to identify the true classifier with accuracy; (iv) convergence of
estimated classifier to the true classifier when the observed label is not
corrupted by noise; (iv) numerical example demonstrating the utility of the
control algorithms.
