Linear-Sized Sensor Scheduling Using Regret Minimization

In this paper, we investigate the problem of time-varying sensor selection for linear time-invariant (LTI) dynamical systems. We develop a framework to design a sparse sensor schedule for a given large-scale LTI system with guaranteed performance bounds using a learning-based algorithm. We show how the observability Gramian matrix of an LTI system can be interpreted as the sum of rank-1 matrices indicating the contribution of the available sensors distributed in time. We then employ a regret minimization framework over density matrices to sparsify this sum of rank-1 matrices to approximate fully sensed LTI dynamics up to a multiplicative factor in some certain observability senses. Our main result provides a linear-sized (in dimension of system) sensor schedule that on the average activates only a constant number of sensors at each time step and significantly improves the previous linearithmic results. Our results naturally apply to the dual problem of actuator selection where a guaranteed approximation to the controllability Gramian will be provided.