Candidate: Alexander Kitaev
Date: September 2, 2025
Time: 11:00am
Location: EIT 3145
Supervisors: Dr. Michael Fisher and Dr. Christopher Nielsen
All are welcome!
Abstract:
The trajectory matching problem is a problem in control theory where a set of reference trajectories for a plant is given, and a control law that causes the plant's trajectories to be as close as possible to the reference trajectories is desired. This thesis presents an approach for solving the trajectory matching problem that generates explicit polynomial controllers. Additionally, the method presented in this thesis guarantees local contractivity of the generated controller.
This thesis presents several theoretical results that justify the method described here. Firstly, a proof that the local contractivity constraint can be expressed as a set of matrix inequalities is presented. Secondly, a theorem that describes how symmetries in the trajectory matching problem correspond to symmetries in its solution is presented and proven.
Finally, this thesis demonstrates the method it describes on two example problems motivated by real-world applications. The first of these is stabilization and disturbance recovery for a single-machine infinite-bus (SMIB) power system, and the second is a lane change manoeuvre for Dubin's vehicle, a simple vehicle model.