Online Optimization and Control
Tracking Error Analysis of Online Optimization Algorithms:
This work covers the development of a unified framework for analyzing the tracking error (the norm of the difference between the optimal solution and the iterate) of first-order online optimization methods in a variety of settings. Specifically, we leverage quadratic constraints to formulate sequential semidefinite programs (SDPs) whose feasible points lead to tracking error bounds of various online optimization methods.
Online Non-stochastic Control vs. Retrospective Cost Adaptive Control :
This work is focused on the study of the online optimization for the design of adaptive controllers in the presence of unknown disturbances and a similar control theoretic framework called Retrospective Cost Adaptive Control (RCAC). We analyze the connections between online non-stochastic control and RCAC in the context of controlling linear dynamical systems subject to unknown non-stochastic disturbances.