On sensor scheduling via information theoretic criteria

We prove the optimality of open-loop control for the sensor scheduling problem of linear Gauss Markov systems using information theoretic criteria. We use dynamic programming arguments to show the data independence on the design of the controller when the objective is to maximize the information about the underlying hidden state. The aim is to compute the sequence of active sensors, using information theoretic criteria, such that the information on the state of the underlying system is maximized. In the second part of the paper, we propose a scheme that considerably reduces the computational burden in computing optimal open-loop sensor schedules. Our scheme is basically an enumeration scheme with optimal pruning. Exploiting a special property of the Riccati equation, we can ignore sensor schedules without the possibility of deleting the optimal sensor sequence