Learning to Control Under Communication Constraints

How to effectively communicate over wireless networks characterized by link failures is central to understanding the fundamental limits in the performance of a networked control system. In this letter, we study the online remote control of linear-quadratic Gaussian systems over unreliable wireless channels (with random packet drops), where the controller is a priori oblivious to the cost parameters. We first reformulate the problem using a semi-definite program and consequently compute a stabilizing policy from its solution. We then derive a O(-T) regret bound (against a best offline policy in hindsight) for a projected online gradient algorithm, where T is the length of the horizon of interest. In the process, we introduce finite-time notions of the classical mean-square stability, which may be of independent interest. Finally, we provide a numerical example to validate the theoretical results, demonstrating the limitations induced by lossy communication on the control performance.