Myopic control of systems with unknown dynamics

This paper introduces a strategy for satisfying basic control objectives for systems whose dynamics are almost entirely unknown. This setting is motivated by a scenario where a system undergoes a critical failure, thus significantly changing its dynamics. In such a case, retaining the ability to satisfy basic control objectives such as reach-avoid is imperative. To deal with significant restrictions on our knowledge of system dynamics, we develop a theory of myopic control. The primary goal of myopic control is to, at any given time, optimize the current direction of the system trajectory, given solely the limited information obtained about the system until that time. Building upon this notion, we propose a control algorithm which simultaneously uses small perturbations in the control effort to learn local system dynamics while moving in the direction which seems to be optimal based on previously obtained knowledge. We show that the algorithm results in a trajectory that is nearly optimal in the myopic sense, i.e., it is moving in a direction that seems to be nearly the best at the given time, and provide formal bounds for suboptimality. We demonstrate the usefulness of the proposed algorithm on a high-fidelity simulation of a damaged Boeing 747 seeking to remain in level flight.