Deterministic Polynomial-Time Actuator Scheduling With Guaranteed Performance

In this paper, the problem of time-varying actuator selection for linear dynamical systems is investigated. By leveraging recent advances in the graph sparsification literature, we develop a framework for designing a sparse actuator schedule for a given large-scale linear system with guaranteed performance bounds using a polynomial-time algorithm. Current approaches based on polynomial time relaxations of the subset selection problem require an extra multiplicative factor of log n sensors/actuators times the minimal number in order to just maintain controllability/observability. In contrast, we show that there exists a polynomial-time actuator schedule that on average selects only a constant number of actuators at each time, to approximate the controllability/observability metrics of the system when all actuators/sensors are in use.