Control-Oriented Learning on the Fly

This article focuses on developing a strategy for control of systems, whose dynamics are almost entirely unknown. This situation arises naturally in a scenario, where a system undergoes a critical failure. In that case, it is imperative to retain the ability to satisfy basic control objectives in order to avert an imminent catastrophe. To deal with limitations on the knowledge of system dynamics, we develop a theory of myopic control. At any given time, myopic control optimizes the current direction of the system trajectory, given solely the knowledge about system dynamics obtained from data until that time. We propose an algorithm that uses small perturbations in the control effort to learn system dynamics around the current system state, while ensuring that the system moves in a nearly optimal direction, and provide bounds for its suboptimality.