Model predictive selection: A receding horizon scheme for actuator selection

We propose a model predictive scheme for selecting actuators in dynamical systems. In control applications, selection problems arise due to the high cost associated to simultaneously using all sensors or actuators in large-scale systems. Since these problems are NP-hard in general, finding an optimal solutions is impractical and approximations based on greedy or convex relaxations are commonly used. In most approaches, however, the control policy and actuator subsets are obtained a priori. In this work, we address the online problem using a model predictive selection (MPS). This iterative procedure inspired by model predictive control methods determines a near-optimal actuator subset for a finite operation horizon starting at the current state, applies the first control action on this subset, and repeats the procedure starting from the new state. Despite using suboptimal solutions of the selection problem, we derive conditions that guarantee this procedure is stable. We illustrate these conditions for the LQR problem by leveraging the concept of approximate submodularity and conclude with numerical experiments that showcase the use of the proposed approach.