The Systems, Cognition, and Control Lab (https://scc.okstate.edu) in the School of Mechanical and Aerospace Engineering at Oklahoma State University is looking for a qualified candidate, preferably with a Master’s or a Bachelor’s degree in pure or applied mathematics. The position is for a research project concerning applications of functional analysis and operator theory to data-driven modeling and control of robotic systems. In this project, the aim is to develop novel operator theoretic techniques for data and model-driven synthesis of control policies through synthesis of CLFs and solution of optimal control problems. The proposed technical tasks focus on the use of trajectories (i.e., time-series) as the fundamental unit of data for the resolution of control synthesis and certification problems in dynamical systems. Trajectory information in the dynamical systems is embedded in a reproducing kernel Hilbert space (RKHS) through what will be called occupation kernels. The occupation kernels are tied to the dynamics of the system through the densely defined Liouville operator. The pairing of Liouville operators and occupation kernels results in an operator theoretic framework that allows for nontrivial information concerning the dynamical systems to be extracted from the RKHS.
For an introduction to the research ideaa pursued in this project, see our preprints https://arxiv.org/abs/1910.03977 and https://arxiv.org/abs/1909.11792.
The project is funded by AFOSR.
Prior experience in analysis including, but not limited to, coursework in advanced calculus, real analysis, and functional analysis will weigh highly in your favor. Once you are here, we will make sure you get the relevant engineering experience to be successful.
If you are interested, please submit an application at https://scc.okstate.edu/apply and select Operator theory, spectral analysis, POD, DMD, Koopman operators, etc. as your topic of interest.