State estimation in networked control systems with delayed and lossy acknowledgments

In this paper, we consider state estimation in Networked Control Systems where both control inputs and measurements are transmitted via networks which are lossy and introduce random transmission delays. In contrast to the common notion of TCP-like communication, where successful transmissions are acknowledged instantaneously and without losses, we focus on the case where the acknowledgment packets provided by the actuator upon reception of applicable control inputs are also subject to delays and losses. Consequently, the estimator has only partial and belated knowledge on the actually applied control inputs, which results in additional uncertainty. We derive an estimator for the considered setup by generalizing an existing approach for UDP-like communication which integrates estimates of the applied control inputs into the overall state estimation. The presented estimator is assessed in terms of Monte Carlo simulations.