Unified Approach to Controller and MMSE Estimator Design with Intermittent Communications

EDWIN PETERS; MARELLI, DAMIAN; MINYUE FU; DANIEL QUEVEDO

Conferencia; IEEE 55th Conference on Decision and Control (CDC); 2016

In this work we consider systems where the mea-surements and control signals are transmitted over networksthat are affected by independent and identically distributed(i.i.d.) packet losses. In this setting, we study two separateproblems. 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 thesystem into account, and are optimal in the sense of minimizinggiven cost functions. It turns out that these two designs, of whicheach has an associated Riccati equation, are dual. We show thatthe convergence of the Riccati equation associated to this dualsystem formulation is a necessary and sufficient condition forstability of the estimator and controller. Finally, we comparethe performance of the proposed offline estimator with thoseof other estimators available from the literature.