So what do I work on in terms of my research? Well, right now it is all about adaptive control and system identification (AC and SI from now on). That is pretty broad, so a more precise description would be AC and SI of systems with nonminimum-phase (NMP) zeros. NMP zeros arise while analyzing certain systems (some systems have NMPs and some do not).

For example, if you take a broom-stick, put it vertically up in the air and try to balance it on your palm, you will notice that if the broom starts moving left, you will need to move your palm to the left as well to “catch up with it” and bring it back to vertical position. Also, you will notice that if you want to move the broom to the right, you first will have to move your palm to the left (to make the broom fall to the right) and only then move your palm to the right to catch up with the broom and bring it back to vertical position. The fact that you have to move in the opposite direction of where you want to go has to do with NMP zeros (more detailed treatment).

NMP zeros are hard to work with in terms of setting up an adaptive controller to solve a command following or disturbance rejection problems. However, our research group is working on an algorithm that can handle NMP zeros, namely Retrospective Cost Adaptive Control (RCAC).

Currently, the part of this research topic that I work on in conjunction with other students is quantifying how well we need to know the NMP zeros for the existing RCAC algorithm, and developing new algorithms that can work without the knowledge of NMP zeros.

To the right you can see a list of papers that I took part in since starting graduate studies at the University of Michigan.