A Separation Principle for Joint Sensor and Actuator Scheduling with Guaranteed Performance Bounds

We study the problem of jointly designing a sparse sensor and actuator schedule for linear dynamical systems while guaranteeing a control/estimation performance that approximates the fully sensed/actuated setting. We further prove a separation principle, showing that the problem can be decomposed into finding sensor and actuator schedules separately. However, it is shown that this problem cannot be efficiently solved or approximated in polynomial, or even quasi-polynomial time for time-invariant sensor/actuator schedules; instead, we develop a framework for a time-varying sensor/actuator schedule for a given large-scale linear system with guaranteed approximation bounds using deterministic polynomial-time algorithms. Our main result is to provide a polynomial-time joint actuator and sensor schedule that on average selects only a constant number of sensors and actuators at each time step, irrespective of the dimension. The key idea is to sparsify the controllability and observability Gramians while providing approximation guarantees for Hankel singular values.