Control and Estimation problems for Nonlinear Systems with an Approximation Theory Framework

The present work aims to contribute towards our understanding of certain classes of estimation and control problems that arise in applications where the governing dynamics are modeled using nonlinear ordinary differential equations and certain functional differential equations that evolve in R^n—H, where R^n is a n-dimensional Euclidean space and H is the Hilbert space. A common theme throughout this talk is to be able to leverage ideas from approximation theory to extend certain conventional adaptive estimation and control frameworks. The first part of the talk delves into estimation and control of history dependent differential equations. This study is motivated by the increasing interest in estimation and control techniques for robotic systems whose governing equations include history dependent nonlinearities such as hysteresis. The second part presents a novel framework for adaptive estimation of nonlinear systems using reproducing kernel Hilbert spaces. In contrast to most conventional strategies for ODEs, the approach here embeds the estimate of the unknown nonlinear function appearing in the plant in a reproducing kernel Hilbert space (RKHS), H. Lastly, some preliminary results are presented to extend the approximation framework to data-driven models in Koopman operator theory.
Parag Bobade graduated with doctoral degree in Engineering Mechanics in Fall 2017. He was advised by Dr. Andrew Kurdila and has worked on research areas spanning topics in adaptive estimation, approximation theory, and functional differential equations. Currently he is interested in exploring and extending the data-driven approaches to dynamical systems governed by functional differential equations and distributed parameter systems.