Learning-Based Actuator Placement for Uncertain Systems

Abstract

In this paper, we develop an online, data-based framework for optimal actuator placement of uncertain systems. In particular, a set of actuators is chosen to maximize a metric of controllability of the system, but without full knowledge of the system’s dynamics, and by only measuring the system’s trajectories in an online manner. The metric of controllability is associated with the trace of a discounted Gramian, which satisfies a static Lyapunov equation even if the system’s plant matrix is not Hurwitz. Subsequently, an estimator is designed to learn the Gramian’s trace exponentially fast in real-time. Finally, we show that the trace estimator can be used to place actuators online, and that the optimal set of actuators is found and scheduled permanently in finite time. The efficacy of the proposed framework is shown through simulations.