Nghia Tran and Dr. Sean Warnick, Computer Science Department
We studied the path control problem, which differ from reference tracking problems in its optimality measure. In general, tracking problems employs the point-wise distance measure, while the path control problem uses the alignment distance. The former is a simple distance measure between particular parameterization of the curves, while the latter measures performance of the path, or the image set, as a whole.
Since path control performance can be made arbitrary good by lengthening the control time, a balance between time and performance is necessary. To deal with that, we formulate the path control problem into two separate problems. In the first problem, one tries to minimize the time while keeping the error bounded, and in the second problem, one tries to minimize the error given a time limit. We proved in our paper submitted to the American Control Conference 2007, that these two formulations were in fact equivalent, that there are solutions to minimize both problems. Also, if we solve the two problems iteratively, the result will converge in no more than two iterations.
We submit our finding regarding the path control problem for the American Control Conference in 2006. Our paper was rejected, with insightful feedbacks. We fixed our paper according to the feedbacks, and submitted to the American Control Conference in 2007. Currently we are still waiting for the decision regarding publication.