Unified approach to controller and MMSE estimator design with intermittent communications

In this work we consider systems where the measurements and control signals are transmitted over networks that are affected by independent and identically distributed (i.i.d.) packet losses. In this setting, we study two separate problems. The first one is the design of an offline state estimator. The second one is the design of a linear quadratic regulator (LQR). Both designs take the statistics of the network and the system into account, and are optimal in the sense of minimizing given cost functions. It turns out that these two designs, of which each has an associated Riccati equation, are dual. We show that the convergence of the Riccati equation associated to this dual system formulation is a necessary and sufficient condition for stability of the estimator and controller. Finally, we compare the performance of the proposed offline estimator with those of other estimators available from the literature.