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.