Online Optimal Tracking of Linear Systems with Adversarial Disturbances

Farnaz Adib Yaghmaie, Hamidreza Modares

Abstract:

This paper presents a memory-augmented control solution to the optimal reference tracking problem for linear systems subject to adversarial disturbances. We assume that the dynamics of the linear system are known and that the reference signal is generated by a linear system
with unknown dynamics. Under these assumptions, finding the optimal tracking controller is formalized as an online convex optimization problem that leverages memory of past disturbance and reference values to capture their temporal effects on the performance. That is, a (disturbance, reference)-action control policy is formalized, which selects the control actions as a linear map of the past disturbance and reference values. The online convex optimization is then formulated over the parameters of the policy on its past disturbance and reference
values to optimize general convex costs. It is shown that our approach outperforms robust control methods and achieves a tight regret bound O(√T) where in our regret analysis, we have benchmarked against the best linear policy.

Submission Length: Long submission (more than 12 pages of main content)

Code: https://github.com/FarnazAdib/online_tracking_with_adversarial_disturbances

Assigned Action Editor: ~Amir-massoud_Farahmand1

License: Creative Commons Attribution 4.0 International (CC BY 4.0)

Submission Number: 645