Optimal Sensor Scheduling for Multiple Linear Dynamical Systems

We consider the design of an optimal collision-free sensor schedule for a number of sensors which monitor different linear dynamical systems correspondingly. At each time, only one of all the sensors can send its local estimate to the remote estimator. A preliminary work for the two-sensor scheduling case has been studied in the literature. The generalization into multiple-sensor scheduling case is shown to be nontrivial. We first find a necessary condition of the optimal solution provided that the spectral radii of any two system matrices are not equal, which can significantly reduce the feasible optimal solution space without loss of performance. By modelling a finite-state Markov decision process (MDP) problem, we can numerically search an asymptotic periodic schedule which is proven to be optimal. From a practical viewpoint, the computational complexity is formidable for some special system models, e.g., the spectral radii of some certain system matrices are far from others'. Some simple but effective suboptimal schedules for any systems are proposed. We also find a lower bound of the optimal cost, which enables us to quantify the performance gap between any suboptimal schedule and the optimal one.